Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21448076 | C2 | semidirect |
| 3. C8×#11758185 | C2 | semidirect |
| 4. C61×#1713 | C2 | semidirect |
| 32. #11758185 | D8 | semidirect |
| 40. C8×C61 | SD32 | semidirect |
| 50. #1713 | D61 | semidirect |
| 63. C61 | #12517 | semidirect |
| 92. C8 | #14519720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448076 | 2 |
| #21445434 | 2 |
| C8×#11758185 | 2 |
| C61×#1713 | 2 |
| #12517 | 61 |