Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21454590 | C2 | semidirect |
| 3. #21447548 | C2 | semidirect |
| 4. #21446708 | C2 | semidirect |
| 5. #21443935 | C2 | semidirect |
| 6. #21443900 | C2 | semidirect |
| 7. C61×#2145 | C2 | semidirect |
| 10. #16840203 | C4 | semidirect |
| 12. #16840198 | C4 | semidirect |
| 50. #14519717 | C2×C4 | semidirect |
| 66. C2×Q16×C61 | C2×C4 | semidirect |
| 68. C2×D8×C61 | C2×C4 | semidirect |
| 188. #2145 | D61 | semidirect |
| 220. C61 | #13027 | semidirect |
| 232. C2×Q16 | C4×D61 | semidirect |
| 236. C2×D8 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| #21454590 | 2 |
| #21447548 | 2 |
| #21446708 | 2 |
| #21443935 | 2 |
| #21443900 | 2 |
| C61×#2145 | 2 |
| #13027 | 61 |