Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. C2×#19153815 | C2 | semidirect |
| 3. #26041687 | C2 | semidirect |
| 4. #26041640 | C2 | semidirect |
| 5. #26041612 | C2 | semidirect |
| 8. #26041562 | C2 | semidirect |
| 9. #26041558 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 11. #484×C181 | C2 | semidirect |
| 128. C181 | #3239 | semidirect |
| 135. #484 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153815 | 2 |
| #26041815 | 2 |
| #26041687 | 2 |
| #26041640 | 2 |
| #26041612 | 2 |
| #26041598 | 2 |
| #26041597 | 2 |
| #26041562 | 2 |
| #26041558 | 2 |
| #26041333 | 2 |
| #484×C181 | 2 |
| #3239 | 181 |