Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
424 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 2. #21462171 | C2 | semidirect |
| 4. #21461937 | C2 | semidirect |
| 5. #21460882 | C2 | semidirect |
| 6. #21460875 | C2 | semidirect |
| 25. #16839576 | C4 | semidirect |
| 26. #16839575 | C4 | semidirect |
| 27. #16839574 | C4 | semidirect |
| 28. C61×#361 | C4 | semidirect |
| 61. #14519717 | C2×C4 | semidirect |
| 64. #14519713 | C2×C4 | semidirect |
| 67. M32×C61 | C2×C4 | semidirect |
| 68. #108×C61 | C2×C4 | semidirect |
| 203. #361 | #6923 | semidirect |
| 206. C61 | #12940 | semidirect |
| 228. M32 | C2×#6923 | semidirect |
| 235. #108 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462578 | 2 |
| #21462171 | 2 |
| C2×#16840674 | 2 |
| #21461937 | 2 |
| #21460882 | 2 |
| #21460875 | 2 |
| #361×D61 | 2 |
| #12940 | 61 |