Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21448544 | C2 | semidirect |
| 3. #21444488 | C2 | semidirect |
| 4. #21444379 | C2 | semidirect |
| 5. #21443679 | C2 | semidirect |
| 6. #21443648 | C2 | semidirect |
| 7. C61×#1963 | C2 | semidirect |
| 10. #16840138 | C4 | semidirect |
| 11. #16840110 | C4 | semidirect |
| 48. C4×#92418 | C2×C4 | semidirect |
| 53. C4⋊Q8×C61 | C2×C4 | semidirect |
| 54. #127×C61 | C2×C4 | semidirect |
| 111. C42×C61 | D8 | semidirect |
| 207. #1963 | D61 | semidirect |
| 238. C61 | #9299 | semidirect |
| 246. C4⋊Q8 | C4×D61 | semidirect |
| 251. #127 | C4×D61 | semidirect |
| 331. C42 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456734 | 2 |
| #21448544 | 2 |
| #21444488 | 2 |
| #21444379 | 2 |
| #21443679 | 2 |
| #21443648 | 2 |
| C61×#1963 | 2 |
| #9299 | 61 |