Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
382 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26042007 | C2 | semidirect |
| 3. #26041644 | C2 | semidirect |
| 4. #26041626 | C2 | semidirect |
| 5. #26041580 | C2 | semidirect |
| 6. #26041560 | C2 | semidirect |
| 7. #26041480 | C2 | semidirect |
| 8. #26041480 | C2 | semidirect |
| 9. #26041381 | C2 | semidirect |
| 10. C4×#15668438 | C2 | semidirect |
| 11. #446×C181 | C2 | semidirect |
| 78. Dic362 | #41 | semidirect |
| 124. C181 | #3368 | semidirect |
| 134. #446 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042007 | 2 |
| #26041951 | 2 |
| #26041644 | 2 |
| #26041626 | 2 |
| #26041580 | 2 |
| #26041560 | 2 |
| #26041480 | 2 |
| #26041381 | 2 |
| C4×#15668438 | 2 |
| #446×C181 | 2 |
| #3368 | 181 |