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. #21455539 | C2 | semidirect |
| 3. #21455481 | C2 | semidirect |
| 4. C2×#16839573 | C2 | semidirect |
| 5. #21447548 | C2 | semidirect |
| 6. #21443918 | C2 | semidirect |
| 7. C61×#2117 | C2 | semidirect |
| 49. C2×Dic244 | D4 | semidirect |
| 53. C2×D488 | D4 | semidirect |
| 66. #14519713 | D4 | semidirect |
| 87. C2×C16×C61 | D4 | semidirect |
| 225. #2117 | D61 | semidirect |
| 259. C61 | #13318 | semidirect |
| 306. C2×C16 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458955 | 2 |
| #21455539 | 2 |
| #21455481 | 2 |
| C2×#16839573 | 2 |
| #21447548 | 2 |
| #21443918 | 2 |
| C61×#2117 | 2 |
| #13318 | 61 |