Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
572 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 572 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. C22×#14519718 | C2 | semidirect |
| 2. #21455467 | C2 | semidirect |
| 3. C2×#16839574 | C2 | semidirect |
| 4. #21447535 | C2 | semidirect |
| 5. C2×#16839546 | C2 | semidirect |
| 6. #21443916 | C2 | semidirect |
| 7. C2×C61×#472 | C2 | semidirect |
| 47. C2×#11758185 | D4 | semidirect |
| 62. C2×D8×C61 | D4 | semidirect |
| 73. #108×C61 | D4 | semidirect |
| 194. C2×#472 | D61 | semidirect |
| 228. C61 | #13319 | semidirect |
| 247. C2×D8 | C22⋊D61 | semidirect |
| 270. #108 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519718 | 2 |
| #21455467 | 2 |
| C2×#16839574 | 2 |
| #21447535 | 2 |
| C2×#16839546 | 2 |
| #21443916 | 2 |
| C2×C61×#472 | 2 |
| #13319 | 61 |