Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16840033 | C2 | semidirect |
| 3. #21455491 | C2 | semidirect |
| 4. C2×#16839568 | C2 | semidirect |
| 5. C2×#16839562 | C2 | semidirect |
| 6. C2×#16839547 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 50. C2×D488 | D4 | semidirect |
| 75. M32×C61 | D4 | semidirect |
| 78. #108×C61 | D4 | semidirect |
| 217. #1387 | D61 | semidirect |
| 249. C61 | #13307 | semidirect |
| 288. M32 | D244 | semidirect |
| 294. #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 |
| C2×#16840033 | 2 |
| #21455491 | 2 |
| C2×#16839568 | 2 |
| C2×#16839562 | 2 |
| C2×#16839547 | 2 |
| C61×#1387 | 2 |
| #13307 | 61 |