Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
826 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 211 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. #21454538 | C2 | semidirect |
| 3. #21446647 | C2 | semidirect |
| 4. #21446145 | C2 | semidirect |
| 5. #21445960 | C2 | semidirect |
| 6. C61×#1745 | C2 | semidirect |
| 10. #16840156 | C4 | semidirect |
| 11. #16840151 | C4 | semidirect |
| 108. #1745 | D61 | semidirect |
| 127. C61 | #22283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456265 | 2 |
| #21454538 | 2 |
| #21446647 | 2 |
| #21446145 | 2 |
| #21445960 | 2 |
| C61×#1745 | 2 |
| #22283 | 61 |