Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 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. #26042003 | C2 | semidirect |
| 2. #26041949 | C2 | semidirect |
| 3. #26041665 | C2 | semidirect |
| 4. #26041496 | C2 | semidirect |
| 5. #26041481 | C2 | semidirect |
| 6. #26041477 | C2 | semidirect |
| 7. #26041471 | C2 | semidirect |
| 8. #26041409 | C2 | semidirect |
| 9. #26041380 | C2 | semidirect |
| 10. C4×D1448 | C2 | semidirect |
| 11. #492×C181 | C2 | semidirect |
| 106. C8×C181 | #41 | semidirect |
| 132. C181 | #3397 | semidirect |
| 137. #492 | D181 | semidirect |
| 239. C8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042003 | 2 |
| #26041949 | 2 |
| #26041665 | 2 |
| #26041496 | 2 |
| #26041481 | 2 |
| #26041477 | 2 |
| #26041471 | 2 |
| #26041409 | 2 |
| #26041380 | 2 |
| C4×D1448 | 2 |
| #492×C181 | 2 |
| #3397 | 181 |