Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
336 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #21443990 | C2 | semidirect |
| 4. #21443984 | C2 | semidirect |
| 12. C61×#541 | C4 | semidirect |
| 14. C61×#497 | C4 | semidirect |
| 17. C61×#488 | C4 | semidirect |
| 22. C61×#433 | C4 | semidirect |
| 35. C4⋊Q8×C61 | C2×C4 | semidirect |
| 40. #125×C61 | C2×C4 | semidirect |
| 54. #97×C61 | C2×C4 | semidirect |
| 55. C4×C8×C61 | C2×C4 | semidirect |
| 159. #541 | Dic61 | semidirect |
| 161. #497 | Dic61 | semidirect |
| 164. #488 | Dic61 | semidirect |
| 169. #433 | Dic61 | semidirect |
| 176. C61 | #13610 | semidirect |
| 183. C4⋊Q8 | C2×Dic61 | semidirect |
| 188. #125 | C2×Dic61 | semidirect |
| 208. #97 | C2×Dic61 | semidirect |
| 209. C4×C8 | C2×Dic61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447491 | 2 |
| #21447488 | 2 |
| #21443990 | 2 |
| #21443984 | 2 |
| C61×#3222 | 2 |
| #13610 | 61 |