Finite Group DatabasebetaFinite Group DatabasebetaOrder 18464.
44 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22604428 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C4×#14556313 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22604417 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#14556313 | — | 2 | 1 | no | — |
| 5 | #17987237 | — | 2 | 1 | no | — |
| 6 | Dic1154 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C22⋊D577 | — | 2 | 1 | no | — |
| 8 | C2×Dic577 | — | 2 | 1 | no | — |
| 9 | C4×D577 | C22 | 1 | 1 | yes | characteristic |
| 10 | D4×C577 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C22×C577 | — | 2 | 1 | no | — |
| 12 | C2×D577 | D4 | 1 | 1 | yes | characteristic |
| 13 | #14556313 | — | 2 | 2 | no | — |
| 14 | C4×C577 | C2×C4 | 1 | 1 | yes | characteristic |
| 15 | Dic577 | — | 2 | 1 | no | — |
| 16 | Dic577 | D4 | 1 | 1 | yes | characteristic |
| 17 | C2×C577 | — | 4 | 1 | no | — |
| 18 | C2×C577 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 19 | D577 | — | 2 | 1 | no | — |
| 20 | C577 | #104 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 21 | #104 | — | 577 | 1 | no | maximal, Sylow |
| 22 | #41 | — | 577 | 1 | no | — |
| 23 | M16 | — | 577 | 1 | no | — |
| 24 | C42 | — | 577 | 1 | no | — |
| 25 | Q8 | — | 577 | 1 | no | — |
| 26 | D4 | — | 1154 | 1 | no | — |
| 27 | D4 | #14556313 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×C4 | — | 577 | 1 | no | — |
| 29 | C2×C4 | — | 1154 | 1 | no | — |
| 30 | C2×C4 | — | 1154 | 1 | no | — |
| 31 | C8 | — | 1154 | 1 | no | — |
| 32 | C22 | — | 2 | 1 | no | — |
| 33 | C22 | — | 577 | 1 | no | — |
| 34 | C4 | — | 577 | 1 | no | — |
| 35 | C4 | — | 1154 | 2 | no | — |
| 36 | C4 | — | 1154 | 1 | no | — |
| 37 | C4 | C2×#14556313 | 1 | 1 | yes | characteristic |
| 38 | C2 | — | 4 | 1 | no | — |
| 39 | C2 | — | 1154 | 1 | no | — |
| 40 | C2 | C22⋊#14556313 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22604428 | C2 | semidirect |
| 2. C4×#14556313 | C2 | semidirect |
| 6. Dic1154 | C4 | semidirect |
| 10. D4×C577 | C4 | semidirect |
| 20. C577 | #104 | semidirect |
| 27. D4 | #14556313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22604428 | 2 |
| C4×#14556313 | 2 |
| #22604417 | 2 |
| #104 | 577 |