Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21444352 | C2 | semidirect |
| 4. #21444183 | C2 | semidirect |
| 5. #21443728 | C2 | semidirect |
| 6. #21443695 | C2 | semidirect |
| 27. C61×#484 | C4 | semidirect |
| 28. C61×#481 | C4 | semidirect |
| 32. C61×#451 | C4 | semidirect |
| 33. C61×#448 | C4 | semidirect |
| 227. #484 | Dic61 | semidirect |
| 228. #481 | Dic61 | semidirect |
| 232. #451 | Dic61 | semidirect |
| 233. #448 | Dic61 | semidirect |
| 251. C61 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454881 | 2 |
| #21444375 | 2 |
| #21444352 | 2 |
| #21444183 | 2 |
| #21443728 | 2 |
| #21443695 | 2 |
| C61×#3196 | 2 |
| #9331 | 61 |