Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26042004 | C2 | semidirect |
| 3. #26041650 | C2 | semidirect |
| 4. #26041482 | C2 | semidirect |
| 5. #26041481 | C2 | semidirect |
| 6. #26041477 | C2 | semidirect |
| 7. #26041476 | C2 | semidirect |
| 8. C8×Dic362 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. SD16×Dic181 | C2 | semidirect |
| 11. #492×C181 | C2 | semidirect |
| 80. Dic362 | SD16 | semidirect |
| 105. C8×C181 | #41 | semidirect |
| 128. C181 | #3392 | semidirect |
| 133. #492 | D181 | semidirect |
| 234. C8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042004 | 2 |
| #26041949 | 2 |
| #26041650 | 2 |
| #26041482 | 2 |
| #26041481 | 2 |
| #26041477 | 2 |
| #26041476 | 2 |
| C8×Dic362 | 2 |
| C4×#15668438 | 2 |
| SD16×Dic181 | 2 |
| #492×C181 | 2 |
| #3392 | 181 |