Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
32 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic2824 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D5648 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C32×C353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Dic1412 | — | 2 | 1 | no | — |
| 5 | D2824 | — | 2 | 1 | no | — |
| 6 | C16×C353 | C22 | 1 | 1 | yes | characteristic |
| 7 | Dic706 | — | 4 | 1 | no | — |
| 8 | D1412 | — | 4 | 1 | no | — |
| 9 | C8×C353 | D4 | 1 | 1 | yes | characteristic |
| 10 | C2×D353 | — | 8 | 1 | no | — |
| 11 | C4×C353 | D8 | 1 | 1 | yes | characteristic |
| 12 | Dic353 | — | 8 | 1 | no | — |
| 13 | C2×C353 | D16 | 1 | 1 | yes | characteristic |
| 14 | D353 | — | 16 | 1 | no | — |
| 15 | C353 | SD64 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | SD64 | — | 353 | 1 | no | maximal, Sylow |
| 17 | Q32 | — | 353 | 1 | no | — |
| 18 | D16 | — | 353 | 1 | no | — |
| 19 | C32 | D353 | 1 | 1 | yes | characteristic, complemented |
| 20 | Q16 | — | 706 | 1 | no | — |
| 21 | D8 | — | 706 | 1 | no | — |
| 22 | C16 | C2×D353 | 1 | 1 | yes | characteristic |
| 23 | Q8 | — | 1412 | 1 | no | — |
| 24 | D4 | — | 1412 | 1 | no | — |
| 25 | C8 | D1412 | 1 | 1 | yes | characteristic |
| 26 | C22 | — | 2824 | 1 | no | — |
| 27 | C4 | — | 2824 | 1 | no | — |
| 28 | C4 | D2824 | 1 | 1 | yes | characteristic |
| 29 | C2 | — | 5648 | 1 | no | — |
| 30 | C2 | D5648 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Dic2824 | C2 | semidirect |
| 3. C32×C353 | C2 | semidirect |
| 15. C353 | SD64 | semidirect |
| 19. C32 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic2824 | 2 |
| D5648 | 2 |
| C32×C353 | 2 |
| SD64 | 353 |