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. C22×D976 | C2 | semidirect |
| 2. C2×#16840032 | C2 | semidirect |
| 3. #21455467 | C2 | semidirect |
| 4. C2×#16839576 | C2 | semidirect |
| 5. #21447536 | C2 | semidirect |
| 6. #21443915 | C2 | semidirect |
| 7. C2×C61×#350 | C2 | semidirect |
| 45. C2×D488 | D4 | semidirect |
| 55. #14519713 | D4 | semidirect |
| 74. C2×C16×C61 | D4 | semidirect |
| 198. C2×#350 | D61 | semidirect |
| 228. C61 | #13319 | 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 |
|---|---|
| C22×D976 | 2 |
| C2×#16840032 | 2 |
| #21455467 | 2 |
| C2×#16839576 | 2 |
| #21447536 | 2 |
| #21443915 | 2 |
| C2×C61×#350 | 2 |
| #13319 | 61 |