Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
588 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26012489 | C2 | semidirect |
| 2. #26012483 | C2 | semidirect |
| 3. #26012477 | C2 | semidirect |
| 4. #26012470 | C2 | semidirect |
| 6. D173⋊M16 | C22 | semidirect |
| 7. #19149758 | C22 | semidirect |
| 16. C2×#14583826 | C4 | semidirect |
| 19. C2×#14583825 | C4 | semidirect |
| 24. C2×D4×D173 | C4 | semidirect |
| 26. C22×D4×C173 | C4 | semidirect |
| 151. C173 | #1795 | semidirect |
| 170. C22×D4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012489 | 2 |
| #26012483 | 2 |
| #26012477 | 2 |
| #26012470 | 2 |
| C2×#19149724 | 2 |
| #1795 | 173 |