Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21458968 | C2 | semidirect |
| 2. #21448138 | C2 | semidirect |
| 3. #21448137 | C2 | semidirect |
| 4. #21448129 | C2 | semidirect |
| 5. #21448128 | C2 | semidirect |
| 6. Q64×D61 | C2 | semidirect |
| 7. #21448112 | C2 | semidirect |
| 8. C2×C61×Q64 | C2 | semidirect |
| 106. C2×Q64 | D61 | semidirect |
| 131. C61 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458968 | 2 |
| #21448138 | 2 |
| #21448137 | 2 |
| #21448129 | 2 |
| #21448128 | 2 |
| Q64×D61 | 2 |
| #21448112 | 2 |
| C2×C61×Q64 | 2 |
| #33984 | 61 |