Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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. #26041986 | C2 | semidirect |
| 3. #26041626 | C2 | semidirect |
| 4. #26041593 | C2 | semidirect |
| 5. #26041575 | C2 | semidirect |
| 6. #26041525 | C2 | semidirect |
| 7. #26041480 | C2 | semidirect |
| 8. #26041443 | C2 | semidirect |
| 9. C4×Dic724 | C2 | semidirect |
| 10. #26041281 | C2 | semidirect |
| 11. #436×C181 | C2 | semidirect |
| 128. C181 | #3333 | semidirect |
| 139. #436 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041986 | 2 |
| #26041950 | 2 |
| #26041626 | 2 |
| #26041593 | 2 |
| #26041575 | 2 |
| #26041525 | 2 |
| #26041480 | 2 |
| #26041443 | 2 |
| C4×Dic724 | 2 |
| #26041281 | 2 |
| #436×C181 | 2 |
| #3333 | 181 |