Finite Group DatabasebetaFinite Group DatabasebetaOrder 22688.
36 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4⋊#15667778 | C2 | 1 | 2 | yes | maximal |
| 2 | C8×D709 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#15667778 | — | 2 | 2 | no | — |
| 4 | C4×D709 | C22 | 1 | 1 | yes | characteristic |
| 5 | #19150886 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C8×C709 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×D709 | D4 | 1 | 1 | yes | characteristic |
| 8 | #15667778 | — | 4 | 2 | no | — |
| 9 | C4×C709 | C2×C4 | 1 | 1 | yes | characteristic |
| 10 | Dic709 | Q8 | 1 | 1 | yes | characteristic |
| 11 | C2×C709 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 12 | D709 | D8 | 1 | 1 | yes | characteristic |
| 13 | D709 | Q16 | 1 | 1 | yes | characteristic |
| 14 | C709 | #107 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | #107 | — | 709 | 1 | no | maximal, Sylow |
| 16 | C2×C8 | — | 709 | 1 | no | — |
| 17 | C4⋊C4 | — | 709 | 2 | no | — |
| 18 | C2×C4 | — | 1418 | 2 | no | — |
| 19 | C2×C4 | — | 709 | 1 | no | — |
| 20 | C8 | — | 709 | 1 | no | — |
| 21 | C8 | #15667778 | 1 | 1 | yes | characteristic, complemented |
| 22 | C22 | — | 709 | 1 | no | — |
| 23 | C4 | — | 2836 | 2 | no | — |
| 24 | C4 | — | 709 | 1 | no | — |
| 25 | C4 | C2×#15667778 | 1 | 1 | yes | characteristic |
| 26 | C2 | — | 709 | 1 | no | — |
| 27 | C2 | — | 709 | 1 | no | — |
| 28 | C2 | C4⋊#15667778 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #19150886 | C4 | semidirect |
| 6. C8×C709 | C4 | semidirect |
| 14. C709 | #107 | semidirect |
| 21. C8 | #15667778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊#15667778 | 2 |
| C8×D709 | 2 |
| #107 | 709 |