Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21455540 | C2 | semidirect |
| 3. #21455482 | C2 | semidirect |
| 4. C2×#16839571 | C2 | semidirect |
| 5. #21447546 | C2 | semidirect |
| 6. #21447446 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 50. C2×Dic244 | D4 | semidirect |
| 54. C2×D488 | D4 | semidirect |
| 83. C2×C16×C61 | D4 | semidirect |
| 85. #108×C61 | D4 | semidirect |
| 226. #1383 | D61 | semidirect |
| 259. C61 | #13318 | semidirect |
| 306. C2×C16 | D244 | semidirect |
| 308. #108 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458955 | 2 |
| #21455540 | 2 |
| #21455482 | 2 |
| C2×#16839571 | 2 |
| #21447546 | 2 |
| #21447446 | 2 |
| C61×#1383 | 2 |
| #13318 | 61 |