Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
238 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 74 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. #21461407 | C2 | semidirect |
| 3. #21460851 | C2 | semidirect |
| 4. #21460776 | C2 | semidirect |
| 6. #21460730 | C2 | semidirect |
| 35. #14519721 | C8 | semidirect |
| 64. Dic244 | C2×C8 | semidirect |
| 67. #11758185 | C2×C8 | semidirect |
| 128. C61 | #12043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461407 | 2 |
| D8×#92420 | 2 |
| #21460851 | 2 |
| #21460776 | 2 |
| #21460773 | 2 |
| #21460730 | 2 |
| #21447674 | 2 |
| #12043 | 61 |