Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #26042002 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041606 | C2 | semidirect |
| 5. #26041564 | C2 | semidirect |
| 6. #26041511 | C2 | semidirect |
| 7. #26041479 | C2 | semidirect |
| 8. #26041440 | C2 | semidirect |
| 9. C8×D724 | C2 | semidirect |
| 10. #26041274 | C2 | semidirect |
| 11. C4×Q16×C181 | C2 | semidirect |
| 127. C181 | #3304 | semidirect |
| 137. C4×Q16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042002 | 2 |
| #26041951 | 2 |
| #26041626 | 2 |
| #26041606 | 2 |
| #26041564 | 2 |
| #26041511 | 2 |
| #26041479 | 2 |
| #26041440 | 2 |
| C8×D724 | 2 |
| #26041274 | 2 |
| C4×Q16×C181 | 2 |
| #3304 | 181 |