Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041944 | C2 | semidirect |
| 2. #26041683 | C2 | semidirect |
| 3. #26041558 | C2 | semidirect |
| 4. #26041556 | C2 | semidirect |
| 5. C8×Dic362 | C2 | semidirect |
| 8. #500×C181 | C2 | semidirect |
| 34. D1448 | Q8 | semidirect |
| 51. Dic362 | D8 | semidirect |
| 53. D724 | C2×Q8 | semidirect |
| 66. C8×C181 | C2×Q8 | semidirect |
| 83. C181 | Q8×D8 | semidirect |
| 87. #500 | D181 | semidirect |
| 150. C8 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041944 | 2 |
| #26041683 | 2 |
| #26041558 | 2 |
| #26041556 | 2 |
| C8×Dic362 | 2 |
| C4×D1448 | 2 |
| #26041361 | 2 |
| #500×C181 | 2 |
| Q8×D8 | 181 |