Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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. #26041834 | C2 | semidirect |
| 3. #26041646 | C2 | semidirect |
| 4. #26041642 | C2 | semidirect |
| 5. #26041641 | C2 | semidirect |
| 6. #26041639 | C2 | semidirect |
| 7. #26041638 | C2 | semidirect |
| 8. #26041274 | C2 | semidirect |
| 9. #26041272 | C2 | semidirect |
| 10. #97×D181 | C2 | semidirect |
| 11. #489×C181 | C2 | semidirect |
| 137. C181 | #3135 | semidirect |
| 146. #489 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| #26041828 | 2 |
| #26041646 | 2 |
| #26041642 | 2 |
| #26041641 | 2 |
| #26041639 | 2 |
| #26041638 | 2 |
| #26041274 | 2 |
| #26041272 | 2 |
| #97×D181 | 2 |
| #489×C181 | 2 |
| #3135 | 181 |