Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
550 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21445581 | C2 | semidirect |
| 3. #21443643 | C2 | semidirect |
| 4. #21443639 | C2 | semidirect |
| 5. C4×C22⋊C8×C61 | C2 | semidirect |
| 184. C4×C22⋊C8 | D61 | semidirect |
| 213. C61 | #7674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454150 | 2 |
| #21445581 | 2 |
| #21443643 | 2 |
| #21443639 | 2 |
| C4×C22⋊C8×C61 | 2 |
| #7674 | 61 |