Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
214 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 92 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×D61⋊C32 | C2 | semidirect |
| 2. C22×#14519827 | C2 | semidirect |
| 3. #21460977 | C2 | semidirect |
| 4. #21460933 | C2 | semidirect |
| 5. C22⋊#14519827 | C2 | semidirect |
| 6. #21460924 | C2 | semidirect |
| 24. #14519827 | D4 | semidirect |
| 66. C22⋊D61 | C32 | semidirect |
| 80. C22×C61 | C2×C32 | semidirect |
| 84. C2×D61 | C2×C32 | semidirect |
| 90. Dic61 | C2×C32 | semidirect |
| 116. C61 | D4×C32 | semidirect |
| 178. C22 | D61⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D61⋊C32 | 2 |
| C22×#14519827 | 2 |
| #21460977 | 2 |
| #21460933 | 2 |
| C22⋊#14519827 | 2 |
| #21460924 | 2 |
| #21447636 | 2 |
| D4×C32 | 61 |