Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
490 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21446283 | C2 | semidirect |
| 2. #21446258 | C2 | semidirect |
| 3. #21446023 | C2 | semidirect |
| 4. #21444387 | C2 | semidirect |
| 5. #21444179 | C2 | semidirect |
| 6. #21443724 | C2 | semidirect |
| 253. C61 | #10560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446283 | 2 |
| #21446258 | 2 |
| #21446023 | 2 |
| #21444387 | 2 |
| #21444179 | 2 |
| #21443724 | 2 |
| C61×#3192 | 2 |
| #10560 | 61 |