Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16840200 | C2 | semidirect |
| 2. #21455540 | C2 | semidirect |
| 3. #21455468 | C2 | semidirect |
| 4. C2×#16839574 | C2 | semidirect |
| 5. #21447554 | C2 | semidirect |
| 6. #21447448 | C2 | semidirect |
| 7. C61×#1389 | C2 | semidirect |
| 43. C2×Dic244 | D4 | semidirect |
| 51. C2×D488 | D4 | semidirect |
| 75. M32×C61 | D4 | semidirect |
| 78. #108×C61 | D4 | semidirect |
| 211. #1389 | D61 | semidirect |
| 242. C61 | #13310 | semidirect |
| 283. M32 | D244 | semidirect |
| 287. #108 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840200 | 2 |
| #21455540 | 2 |
| #21455468 | 2 |
| C2×#16839574 | 2 |
| #21447554 | 2 |
| #21447448 | 2 |
| C61×#1389 | 2 |
| #13310 | 61 |