Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041622 | C2 | semidirect |
| 4. #26041561 | C2 | semidirect |
| 5. #26041490 | C2 | semidirect |
| 6. #26041484 | C2 | semidirect |
| 8. #26041373 | C2 | semidirect |
| 9. #26041370 | C2 | semidirect |
| 10. #26041331 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 136. C181 | #3107 | semidirect |
| 142. #474 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| C4×#15668448 | 2 |
| #26041622 | 2 |
| #26041561 | 2 |
| #26041490 | 2 |
| #26041484 | 2 |
| #26041442 | 2 |
| #26041373 | 2 |
| #26041370 | 2 |
| #26041331 | 2 |
| #474×C181 | 2 |
| #3107 | 181 |