Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic724 | C2 | semidirect |
| 3. #26041659 | C2 | semidirect |
| 4. #26041520 | C2 | semidirect |
| 5. #26041490 | C2 | semidirect |
| 6. #26041437 | C2 | semidirect |
| 7. C4×Dic724 | C2 | semidirect |
| 38. Dic724 | D4 | direct (N × H) |
| 65. D4×C181 | Q16 | semidirect |
| 77. C22×C181 | C2×Q16 | semidirect |
| 81. C4×C181 | C2×Q16 | semidirect |
| 91. C181 | D4×Q16 | semidirect |
| 153. D4 | Dic724 | direct (N × H) |
| 169. C22 | C2×Dic724 | semidirect |
| 176. C4 | C2×Dic724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic724 | 2 |
| D4×Dic362 | 2 |
| #26041659 | 2 |
| #26041520 | 2 |
| #26041490 | 2 |
| #26041437 | 2 |
| C4×Dic724 | 2 |
| C8×D4×C181 | 2 |
| D4×Q16 | 181 |