Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 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. #26041999 | C2 | semidirect |
| 2. D4×Dic362 | C2 | semidirect |
| 3. #26041637 | C2 | semidirect |
| 4. #26041630 | C2 | semidirect |
| 5. #26041573 | C2 | semidirect |
| 6. #26041559 | C2 | semidirect |
| 8. #26041484 | C2 | semidirect |
| 9. #26041409 | C2 | semidirect |
| 10. #26041376 | C2 | semidirect |
| 122. C181 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041999 | 2 |
| D4×Dic362 | 2 |
| #26041637 | 2 |
| #26041630 | 2 |
| #26041573 | 2 |
| #26041559 | 2 |
| #26041492 | 2 |
| #26041484 | 2 |
| #26041409 | 2 |
| #26041376 | 2 |
| C4×D8×C181 | 2 |
| #3367 | 181 |