Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
402 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 158 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. #26042304 | C2 | semidirect |
| 2. #26042300 | C2 | semidirect |
| 3. #26042296 | C2 | semidirect |
| 4. #26042286 | C2 | semidirect |
| 7. #26042244 | C2 | semidirect |
| 11. #19153883 | C22 | semidirect |
| 12. C4⋊#13089685 | C22 | semidirect |
| 18. #19153871 | C22 | semidirect |
| 19. C4×#13089685 | C22 | semidirect |
| 110. C181 | #2924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042304 | 2 |
| #26042300 | 2 |
| #26042296 | 2 |
| #26042286 | 2 |
| #26042250 | 2 |
| D181⋊(C22⋊C8) | 2 |
| #26042244 | 2 |
| C2×#19153774 | 2 |
| #2924 | 181 |