Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26041642 | C2 | semidirect |
| 4. #26041581 | C2 | semidirect |
| 5. #26041556 | C2 | semidirect |
| 6. #26041478 | C2 | semidirect |
| 7. #26041476 | C2 | semidirect |
| 8. #26041409 | C2 | semidirect |
| 9. #26041376 | C2 | semidirect |
| 10. C4×#15668438 | C2 | semidirect |
| 11. #486×C181 | C2 | semidirect |
| 77. Dic362 | #41 | semidirect |
| 124. C181 | #3368 | semidirect |
| 129. #486 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042004 | 2 |
| #26041949 | 2 |
| #26041642 | 2 |
| #26041581 | 2 |
| #26041556 | 2 |
| #26041478 | 2 |
| #26041476 | 2 |
| #26041409 | 2 |
| #26041376 | 2 |
| C4×#15668438 | 2 |
| #486×C181 | 2 |
| #3368 | 181 |