Finite Group DatabasebetaFinite Group DatabasebetaOrder 22432.
38 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#19150487 | C2 | 1 | 2 | yes | maximal |
| 2 | C4×Dic701 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #19150487 | — | 2 | 2 | no | — |
| 4 | C2×Dic701 | C4 | 1 | 1 | yes | characteristic |
| 5 | C2×Dic701 | C22 | 1 | 1 | yes | characteristic |
| 6 | C2×C4×C701 | C4 | 1 | 1 | yes | characteristic |
| 7 | C22×C701 | C2×C4 | 1 | 1 | yes | characteristic |
| 8 | C4×C701 | — | 2 | 1 | no | — |
| 9 | Dic701 | C8 | 1 | 2 | yes | complemented |
| 10 | Dic701 | D4 | 1 | 1 | yes | characteristic |
| 11 | Dic701 | Q8 | 1 | 1 | yes | characteristic |
| 12 | C2×C701 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 13 | C2×C701 | C2×C8 | 1 | 1 | yes | characteristic |
| 14 | C2×C701 | M16 | 1 | 1 | yes | characteristic |
| 15 | C701 | C4⋊C8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C4⋊C8 | — | 701 | 1 | no | maximal, Sylow |
| 17 | C2×C8 | — | 701 | 2 | no | — |
| 18 | C42 | — | 701 | 1 | no | — |
| 19 | C2×C4 | — | 701 | 1 | no | — |
| 20 | C2×C4 | — | 701 | 1 | no | — |
| 21 | C2×C4 | #14584149 | 1 | 1 | yes | characteristic |
| 22 | C8 | — | 1402 | 2 | no | — |
| 23 | C22 | C2×#14584149 | 1 | 1 | yes | characteristic |
| 24 | C4 | — | 2 | 1 | no | — |
| 25 | C4 | — | 701 | 1 | no | — |
| 26 | C4 | — | 701 | 1 | no | — |
| 27 | C4 | — | 701 | 2 | no | — |
| 28 | C2 | C4⋊#14584149 | 1 | 1 | yes | characteristic |
| 29 | C2 | D701⋊C8 | 1 | 1 | yes | characteristic |
| 30 | C2 | #26014315 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. Dic701 | C8 | semidirect |
| 15. C701 | C4⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150487 | 2 |
| C4×Dic701 | 2 |
| C4⋊C8 | 701 |