Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26042008 | C2 | semidirect |
| 3. #26041642 | C2 | semidirect |
| 4. #26041625 | C2 | semidirect |
| 5. #26041577 | C2 | semidirect |
| 6. #26041560 | C2 | semidirect |
| 7. #26041477 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 9. #26041380 | C2 | semidirect |
| 10. C4×#15668436 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 91. Q8×C181 | #41 | semidirect |
| 124. C181 | #3368 | semidirect |
| 133. #460 | D181 | semidirect |
| 204. Q8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042008 | 2 |
| #26041949 | 2 |
| #26041642 | 2 |
| #26041625 | 2 |
| #26041577 | 2 |
| #26041560 | 2 |
| #26041477 | 2 |
| #26041406 | 2 |
| #26041380 | 2 |
| C4×#15668436 | 2 |
| #460×C181 | 2 |
| #3368 | 181 |