Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26042012 | C2 | semidirect |
| 2. #26041663 | C2 | semidirect |
| 3. #26041662 | C2 | semidirect |
| 5. #26041494 | C2 | semidirect |
| 6. #26041493 | C2 | semidirect |
| 7. #26041478 | C2 | semidirect |
| 8. C8×Dic362 | C2 | semidirect |
| 9. #26041373 | C2 | semidirect |
| 10. #26041361 | C2 | semidirect |
| 11. C4×D8×C181 | C2 | semidirect |
| 120. C181 | #3396 | semidirect |
| 132. C4×D8 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042012 | 2 |
| #26041663 | 2 |
| #26041662 | 2 |
| #26041654 | 2 |
| #26041494 | 2 |
| #26041493 | 2 |
| #26041478 | 2 |
| C8×Dic362 | 2 |
| #26041373 | 2 |
| #26041361 | 2 |
| C4×D8×C181 | 2 |
| #3396 | 181 |