Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 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. C2×#16840029 | C2 | semidirect |
| 2. #21455463 | C2 | semidirect |
| 3. C2×#16839575 | C2 | semidirect |
| 4. #21447535 | C2 | semidirect |
| 5. C2×#16839545 | C2 | semidirect |
| 6. #21443915 | C2 | semidirect |
| 7. C22×D16×C61 | C2 | semidirect |
| 51. #14519713 | D4 | semidirect |
| 69. C2×D8×C61 | D4 | semidirect |
| 74. C2×C16×C61 | D4 | semidirect |
| 193. C22×D16 | D61 | semidirect |
| 228. C61 | #13319 | semidirect |
| 247. C2×D8 | C22⋊D61 | semidirect |
| 268. C2×C16 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840029 | 2 |
| #21455463 | 2 |
| C2×#16839575 | 2 |
| #21447535 | 2 |
| C2×#16839545 | 2 |
| #21443915 | 2 |
| C22×D16×C61 | 2 |
| #13319 | 61 |