Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 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. C2×#16840200 | C2 | semidirect |
| 2. #21455539 | C2 | semidirect |
| 3. #21455467 | C2 | semidirect |
| 4. C2×#16839576 | C2 | semidirect |
| 5. #21447556 | C2 | semidirect |
| 6. #21443934 | C2 | semidirect |
| 7. C61×#2117 | C2 | semidirect |
| 42. C2×Dic244 | D4 | semidirect |
| 50. C2×D488 | D4 | semidirect |
| 60. #14519713 | D4 | semidirect |
| 78. M32×C61 | D4 | semidirect |
| 210. #2117 | D61 | semidirect |
| 242. C61 | #13310 | semidirect |
| 283. M32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840200 | 2 |
| #21455539 | 2 |
| #21455467 | 2 |
| C2×#16839576 | 2 |
| #21447556 | 2 |
| #21443934 | 2 |
| C61×#2117 | 2 |
| #13310 | 61 |