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. #26042003 | C2 | semidirect |
| 2. D4×Dic362 | C2 | semidirect |
| 3. #26041640 | C2 | semidirect |
| 4. #26041629 | C2 | semidirect |
| 5. #26041572 | C2 | semidirect |
| 6. #26041560 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 9. #26041380 | C2 | semidirect |
| 11. #461×C181 | C2 | semidirect |
| 122. C181 | #3367 | semidirect |
| 131. #461 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042003 | 2 |
| D4×Dic362 | 2 |
| #26041640 | 2 |
| #26041629 | 2 |
| #26041572 | 2 |
| #26041560 | 2 |
| #26041496 | 2 |
| #26041406 | 2 |
| #26041380 | 2 |
| C4×#15668434 | 2 |
| #461×C181 | 2 |
| #3367 | 181 |