Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21448106 | C2 | semidirect |
| 3. #21445337 | C2 | semidirect |
| 4. #21443871 | C2 | semidirect |
| 5. #21443801 | C2 | semidirect |
| 68. D8×C61 | Q16 | semidirect |
| 162. C61 | #12414 | semidirect |
| 205. D8 | #11758202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448106 | 2 |
| #21447966 | 2 |
| #21445337 | 2 |
| #21443871 | 2 |
| #21443801 | 2 |
| #21443786 | 2 |
| C61×#3389 | 2 |
| #12414 | 61 |