Finite Group DatabasebetaFinite Group DatabasebetaOrder 23888.
26 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×Dic1493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×Dic1493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C4×C1493 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C22×C1493 | C22 | 1 | 1 | yes | characteristic |
| 5 | C4×C1493 | — | 2 | 1 | no | — |
| 6 | Dic1493 | — | 2 | 1 | no | — |
| 7 | Dic1493 | C4 | 1 | 2 | yes | complemented |
| 8 | C2×C1493 | C2×C4 | 1 | 1 | yes | characteristic |
| 9 | C2×C1493 | D4 | 1 | 1 | yes | characteristic |
| 10 | C2×C1493 | Q8 | 1 | 1 | yes | characteristic |
| 11 | C1493 | C4⋊C4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | C4⋊C4 | — | 1493 | 1 | no | maximal, Sylow |
| 13 | C2×C4 | — | 1493 | 1 | no | — |
| 14 | C2×C4 | — | 1493 | 1 | no | — |
| 15 | C2×C4 | D1493 | 1 | 1 | yes | characteristic |
| 16 | C22 | C2×D1493 | 1 | 1 | yes | characteristic |
| 17 | C4 | — | 2 | 1 | no | — |
| 18 | C4 | — | 2986 | 1 | no | — |
| 19 | C4 | — | 1493 | 2 | no | — |
| 20 | C2 | C4×D1493 | 1 | 1 | yes | characteristic |
| 21 | C2 | C22⋊D1493 | 1 | 1 | yes | characteristic |
| 22 | C2 | Dic2986 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. Dic1493 | C4 | semidirect |
| 11. C1493 | C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1493 | 2 |
| C2×C4×C1493 | 2 |
| C4⋊C4 | 1493 |