Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
706 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 3. #21445436 | C2 | semidirect |
| 4. #21445429 | C2 | semidirect |
| 5. #21445415 | C2 | semidirect |
| 7. C61×#1710 | C2 | semidirect |
| 70. C8×D61 | Q16 | semidirect |
| 100. #1710 | D61 | semidirect |
| 123. C61 | #19604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456404 | 2 |
| #21456330 | 2 |
| #21445436 | 2 |
| #21445429 | 2 |
| #21445415 | 2 |
| C82×D61 | 2 |
| C61×#1710 | 2 |
| #19604 | 61 |