Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041999 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041604 | C2 | semidirect |
| 5. #26041565 | C2 | semidirect |
| 6. #26041508 | C2 | semidirect |
| 7. #26041480 | C2 | semidirect |
| 8. #26041443 | C2 | semidirect |
| 9. C4×Dic724 | C2 | semidirect |
| 10. #26041276 | C2 | semidirect |
| 11. C8×D4×C181 | C2 | semidirect |
| 127. C181 | #3304 | semidirect |
| 138. C8×D4 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041999 | 2 |
| #26041950 | 2 |
| #26041626 | 2 |
| #26041604 | 2 |
| #26041565 | 2 |
| #26041508 | 2 |
| #26041480 | 2 |
| #26041443 | 2 |
| C4×Dic724 | 2 |
| #26041276 | 2 |
| C8×D4×C181 | 2 |
| #3304 | 181 |