Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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. D4×Dic362 | C2 | semidirect |
| 2. #26041684 | C2 | semidirect |
| 3. #26041683 | C2 | semidirect |
| 4. #26041559 | C2 | semidirect |
| 5. #26041557 | C2 | semidirect |
| 6. C8×Dic362 | C2 | semidirect |
| 43. D8×C181 | Q8 | semidirect |
| 51. Dic362 | D8 | direct (N × H) |
| 59. D4×C181 | C2×Q8 | semidirect |
| 66. C8×C181 | C2×Q8 | semidirect |
| 83. C181 | Q8×D8 | semidirect |
| 119. D8 | Dic362 | direct (N × H) |
| 138. D4 | C2×Dic362 | semidirect |
| 150. C8 | C2×Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic362 | 2 |
| #26041684 | 2 |
| #26041683 | 2 |
| #26041559 | 2 |
| #26041557 | 2 |
| C8×Dic362 | 2 |
| D8×Dic181 | 2 |
| C4×D8×C181 | 2 |
| Q8×D8 | 181 |