Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 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 |
|---|---|---|
| 1. #21455279 | C2 | semidirect |
| 2. #21450766 | C2 | semidirect |
| 3. #21444487 | C2 | semidirect |
| 4. #21444314 | C2 | semidirect |
| 5. #21444209 | C2 | semidirect |
| 6. #21443721 | C2 | semidirect |
| 7. C61×#3205 | C2 | semidirect |
| 53. C4⋊#92418 | D4 | semidirect |
| 64. C4⋊Q8×C61 | D4 | semidirect |
| 69. #127×C61 | D4 | semidirect |
| 76. C4⋊C8×C61 | D4 | semidirect |
| 117. C2×D244 | D8 | semidirect |
| 233. #3205 | D61 | semidirect |
| 271. C61 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D61 | semidirect |
| 292. #127 | C22⋊D61 | semidirect |
| 312. C4⋊C8 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455279 | 2 |
| #21450766 | 2 |
| #21444487 | 2 |
| #21444314 | 2 |
| #21444209 | 2 |
| #21443721 | 2 |
| C61×#3205 | 2 |
| #10238 | 61 |