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. #21458969 | C2 | semidirect |
| 2. #21448136 | C2 | semidirect |
| 3. #21448135 | C2 | semidirect |
| 4. #21448125 | C2 | semidirect |
| 5. C2×Dic976 | C2 | semidirect |
| 6. Q64×D61 | C2 | semidirect |
| 7. #21448112 | C2 | semidirect |
| 8. C61×#2262 | C2 | semidirect |
| 104. #2262 | 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 |
|---|---|
| #21458969 | 2 |
| #21448136 | 2 |
| #21448135 | 2 |
| #21448125 | 2 |
| C2×Dic976 | 2 |
| Q64×D61 | 2 |
| #21448112 | 2 |
| C61×#2262 | 2 |
| #33984 | 61 |