Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #26041829 | C2 | semidirect |
| 2. #26041813 | C2 | semidirect |
| 3. #26041673 | C2 | semidirect |
| 4. #26041668 | C2 | semidirect |
| 5. #26041648 | C2 | semidirect |
| 6. #26041644 | C2 | semidirect |
| 7. #26041502 | C2 | semidirect |
| 8. #26041495 | C2 | semidirect |
| 9. #26041443 | C2 | semidirect |
| 10. #26041426 | C2 | semidirect |
| 11. #432×C181 | C2 | semidirect |
| 140. C181 | #3219 | semidirect |
| 152. #432 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041813 | 2 |
| #26041673 | 2 |
| #26041668 | 2 |
| #26041648 | 2 |
| #26041644 | 2 |
| #26041502 | 2 |
| #26041495 | 2 |
| #26041443 | 2 |
| #26041426 | 2 |
| #432×C181 | 2 |
| #3219 | 181 |