Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
756 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 215 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. #21446308 | C2 | semidirect |
| 2. #21446301 | C2 | semidirect |
| 3. #21446218 | C2 | semidirect |
| 4. #21446203 | C2 | semidirect |
| 5. #21445968 | C2 | semidirect |
| 20. C61×#496 | C4 | semidirect |
| 21. C61×#493 | C4 | semidirect |
| 22. C61×#492 | C4 | semidirect |
| 39. C2×SD16×C61 | C2×C4 | semidirect |
| 40. C2×D8×C61 | C2×C4 | semidirect |
| 42. C4⋊Q8×C61 | C2×C4 | semidirect |
| 46. #127×C61 | C2×C4 | semidirect |
| 47. #124×C61 | C2×C4 | semidirect |
| 51. #97×C61 | C2×C4 | semidirect |
| 52. C4×C8×C61 | C2×C4 | semidirect |
| 148. #496 | Dic61 | semidirect |
| 149. #493 | Dic61 | semidirect |
| 150. #492 | Dic61 | semidirect |
| 160. C61 | #23361 | semidirect |
| 166. C2×SD16 | C2×Dic61 | semidirect |
| 167. C2×D8 | C2×Dic61 | semidirect |
| 172. C4⋊Q8 | C2×Dic61 | semidirect |
| 176. #127 | C2×Dic61 | semidirect |
| 177. #124 | C2×Dic61 | semidirect |
| 188. #97 | C2×Dic61 | semidirect |
| 189. C4×C8 | C2×Dic61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446308 | 2 |
| #21446301 | 2 |
| #21446218 | 2 |
| #21446203 | 2 |
| #21445968 | 2 |
| C61×#3151 | 2 |
| #23361 | 61 |