Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
254 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 254 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. #21461400 | C2 | semidirect |
| 2. D8×#92420 | C2 | semidirect |
| 3. #21460853 | C2 | semidirect |
| 4. #21460774 | C2 | semidirect |
| 5. #21460773 | C2 | semidirect |
| 6. #21460730 | C2 | semidirect |
| 35. #14519718 | C8 | semidirect |
| 56. D8×C61 | C2×C8 | semidirect |
| 65. D488 | C2×C8 | semidirect |
| 68. #11758185 | C2×C8 | semidirect |
| 134. C61 | #12045 | semidirect |
| 163. D8 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461400 | 2 |
| D8×#92420 | 2 |
| #21460853 | 2 |
| #21460774 | 2 |
| #21460773 | 2 |
| #21460730 | 2 |
| #21447663 | 2 |
| #12045 | 61 |