Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21458955 | C2 | semidirect |
| 2. C2×#16840200 | C2 | semidirect |
| 3. #21456305 | C2 | semidirect |
| 4. #21447556 | C2 | semidirect |
| 5. #21447536 | C2 | semidirect |
| 6. #21446717 | C2 | semidirect |
| 7. C61×#1378 | C2 | semidirect |
| 47. C2×Dic244 | D4 | semidirect |
| 59. C2×D488 | D4 | semidirect |
| 81. M32×C61 | D4 | semidirect |
| 83. C2×C16×C61 | D4 | semidirect |
| 217. #1378 | D61 | semidirect |
| 250. C61 | #13334 | semidirect |
| 295. M32 | D244 | semidirect |
| 297. C2×C16 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458955 | 2 |
| C2×#16840200 | 2 |
| #21456305 | 2 |
| #21447556 | 2 |
| #21447536 | 2 |
| #21446717 | 2 |
| C61×#1378 | 2 |
| #13334 | 61 |