Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21458953 | C2 | semidirect |
| 2. #21455400 | C2 | semidirect |
| 3. #21447555 | C2 | semidirect |
| 4. #21447554 | C2 | semidirect |
| 5. #21447430 | C2 | semidirect |
| 6. #21443920 | C2 | semidirect |
| 7. C61×#3050 | C2 | semidirect |
| 38. C2×Dic244 | D4 | semidirect |
| 40. C2×D488 | D4 | semidirect |
| 56. C2×#11758185 | D4 | semidirect |
| 58. #14519709 | D4 | semidirect |
| 67. C2×Q16×C61 | D4 | semidirect |
| 69. C2×D8×C61 | D4 | semidirect |
| 85. #106×C61 | D4 | semidirect |
| 228. #3050 | D61 | semidirect |
| 265. C61 | #13309 | semidirect |
| 278. C2×Q16 | C22⋊D61 | semidirect |
| 282. C2×D8 | C22⋊D61 | semidirect |
| 316. #106 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| #21455400 | 2 |
| #21447555 | 2 |
| #21447554 | 2 |
| #21447430 | 2 |
| #21443920 | 2 |
| C61×#3050 | 2 |
| #13309 | 61 |