Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19153849 | C2 | semidirect |
| 2. #26041938 | C2 | semidirect |
| 3. #26041663 | C2 | semidirect |
| 4. #26041525 | C2 | semidirect |
| 5. #26041502 | C2 | semidirect |
| 6. #26041437 | C2 | semidirect |
| 7. #26041426 | C2 | semidirect |
| 8. C4×Dic724 | C2 | semidirect |
| 9. #436×C181 | C2 | semidirect |
| 50. Dic724 | D4 | semidirect |
| 117. C181 | #3277 | semidirect |
| 127. #436 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153849 | 2 |
| #26041938 | 2 |
| #26041663 | 2 |
| #26041525 | 2 |
| #26041502 | 2 |
| #26041437 | 2 |
| #26041426 | 2 |
| C4×Dic724 | 2 |
| #436×C181 | 2 |
| #3277 | 181 |