Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21454702 | C2 | semidirect |
| 3. #21447554 | C2 | semidirect |
| 4. C2×#16839571 | C2 | semidirect |
| 5. #21446715 | C2 | semidirect |
| 6. #21443906 | C2 | semidirect |
| 7. C61×#1386 | C2 | semidirect |
| 12. #16840205 | C4 | semidirect |
| 14. #16840200 | C4 | semidirect |
| 39. C2×Dic244 | C2×C4 | semidirect |
| 43. C2×D488 | C2×C4 | semidirect |
| 69. M32×C61 | C2×C4 | semidirect |
| 189. #1386 | D61 | semidirect |
| 218. C61 | #13030 | semidirect |
| 252. M32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458955 | 2 |
| #21454702 | 2 |
| #21447554 | 2 |
| C2×#16839571 | 2 |
| #21446715 | 2 |
| #21443906 | 2 |
| C61×#1386 | 2 |
| #13030 | 61 |