Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21454416 | C2 | semidirect |
| 3. #21447534 | C2 | semidirect |
| 4. C2×#16839564 | C2 | semidirect |
| 5. C2×#16839545 | C2 | semidirect |
| 6. #21443929 | C2 | semidirect |
| 7. C61×#1382 | C2 | semidirect |
| 14. #16840033 | C4 | semidirect |
| 39. C2×D488 | C2×C4 | semidirect |
| 68. #108×C61 | C2×C4 | semidirect |
| 188. #1382 | D61 | semidirect |
| 216. C61 | #12996 | semidirect |
| 252. #108 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840033 | 2 |
| #21454416 | 2 |
| #21447534 | 2 |
| C2×#16839564 | 2 |
| C2×#16839545 | 2 |
| #21443929 | 2 |
| C61×#1382 | 2 |
| #12996 | 61 |