Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26041982 | C2 | semidirect |
| 2. #26041606 | C2 | semidirect |
| 3. #26041594 | C2 | semidirect |
| 4. #26041576 | C2 | semidirect |
| 5. #26041533 | C2 | semidirect |
| 6. C4×D1448 | C2 | semidirect |
| 7. #26041358 | C2 | semidirect |
| 8. #26041318 | C2 | semidirect |
| 9. #499×C181 | C2 | semidirect |
| 102. C181 | #3355 | semidirect |
| 105. #499 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041982 | 2 |
| #26041606 | 2 |
| #26041594 | 2 |
| #26041576 | 2 |
| #26041533 | 2 |
| C4×D1448 | 2 |
| #26041358 | 2 |
| #26041318 | 2 |
| #499×C181 | 2 |
| #3355 | 181 |