Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 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. #26042015 | C2 | semidirect |
| 2. #26041949 | C2 | semidirect |
| 3. #26041667 | C2 | semidirect |
| 4. #26041492 | C2 | semidirect |
| 5. #26041476 | C2 | semidirect |
| 6. #26041472 | C2 | semidirect |
| 7. #26041471 | C2 | semidirect |
| 8. #26041409 | C2 | semidirect |
| 9. #26041391 | C2 | semidirect |
| 10. C4×#15668438 | C2 | semidirect |
| 11. #493×C181 | C2 | semidirect |
| 108. C8×C181 | #41 | semidirect |
| 134. C181 | #3399 | semidirect |
| 139. #493 | D181 | semidirect |
| 243. C8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042015 | 2 |
| #26041949 | 2 |
| #26041667 | 2 |
| #26041492 | 2 |
| #26041476 | 2 |
| #26041472 | 2 |
| #26041471 | 2 |
| #26041409 | 2 |
| #26041391 | 2 |
| C4×#15668438 | 2 |
| #493×C181 | 2 |
| #3399 | 181 |