Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21454696 | C2 | semidirect |
| 3. C2×#16839570 | C2 | semidirect |
| 4. C2×#16839564 | C2 | semidirect |
| 5. #21446729 | C2 | semidirect |
| 6. #21443928 | C2 | semidirect |
| 7. C61×#1379 | C2 | semidirect |
| 12. #16840200 | C4 | semidirect |
| 41. C2×D488 | C2×C4 | semidirect |
| 65. M32×C61 | C2×C4 | semidirect |
| 188. #1379 | D61 | semidirect |
| 216. C61 | #13022 | semidirect |
| 245. M32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840200 | 2 |
| #21454696 | 2 |
| C2×#16839570 | 2 |
| C2×#16839564 | 2 |
| #21446729 | 2 |
| #21443928 | 2 |
| C61×#1379 | 2 |
| #13022 | 61 |