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. #26041674 | C2 | semidirect |
| 3. #26041669 | C2 | semidirect |
| 4. #26041649 | C2 | semidirect |
| 5. #26041645 | C2 | semidirect |
| 6. #26041501 | C2 | semidirect |
| 7. #26041494 | C2 | semidirect |
| 8. #26041439 | C2 | semidirect |
| 9. #26041422 | C2 | semidirect |
| 10. #26041336 | C2 | semidirect |
| 11. #529×C181 | C2 | semidirect |
| 140. C181 | #3219 | semidirect |
| 143. #529 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041674 | 2 |
| #26041669 | 2 |
| #26041649 | 2 |
| #26041645 | 2 |
| #26041501 | 2 |
| #26041494 | 2 |
| #26041439 | 2 |
| #26041422 | 2 |
| #26041336 | 2 |
| #529×C181 | 2 |
| #3219 | 181 |