Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21447584 | C2 | semidirect |
| 3. #21447566 | C2 | semidirect |
| 4. #21447534 | C2 | semidirect |
| 5. #21446727 | C2 | semidirect |
| 6. #21446715 | C2 | semidirect |
| 7. C61×#1389 | C2 | semidirect |
| 168. #1389 | D61 | semidirect |
| 194. C61 | #13442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840200 | 2 |
| #21447584 | 2 |
| #21447566 | 2 |
| #21447534 | 2 |
| #21446727 | 2 |
| #21446715 | 2 |
| C61×#1389 | 2 |
| #13442 | 61 |