Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16840197 | C2 | semidirect |
| 3. #21456305 | C2 | semidirect |
| 4. #21447554 | C2 | semidirect |
| 5. #21447534 | C2 | semidirect |
| 6. #21443905 | C2 | semidirect |
| 7. C61×#1976 | C2 | semidirect |
| 65. #14519717 | D4 | semidirect |
| 67. C2×#11758185 | D4 | semidirect |
| 73. C2×Q16×C61 | D4 | semidirect |
| 75. C2×D8×C61 | D4 | semidirect |
| 216. #1976 | D61 | semidirect |
| 250. C61 | #13334 | semidirect |
| 265. C2×Q16 | D244 | semidirect |
| 277. C2×D8 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| C2×#16840197 | 2 |
| #21456305 | 2 |
| #21447554 | 2 |
| #21447534 | 2 |
| #21443905 | 2 |
| C61×#1976 | 2 |
| #13334 | 61 |