Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21454958 | C2 | semidirect |
| 2. #21446747 | C2 | semidirect |
| 3. #21444533 | C2 | semidirect |
| 4. #21444344 | C2 | semidirect |
| 5. #21443688 | C2 | semidirect |
| 6. #21443674 | C2 | semidirect |
| 26. C61×#496 | C4 | semidirect |
| 27. C61×#490 | C4 | semidirect |
| 225. #496 | Dic61 | semidirect |
| 226. #490 | Dic61 | semidirect |
| 248. C61 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454958 | 2 |
| #21446747 | 2 |
| #21444533 | 2 |
| #21444344 | 2 |
| #21443688 | 2 |
| #21443674 | 2 |
| C61×#3217 | 2 |
| #9378 | 61 |