Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462198 | C2 | semidirect |
| 2. D4×#11758187 | C2 | semidirect |
| 3. #21460842 | C2 | semidirect |
| 4. #21460770 | C2 | semidirect |
| 5. D4⋊#11758187 | C2 | semidirect |
| 6. #21460734 | C2 | semidirect |
| 54. #11758199 | C16 | semidirect |
| 74. D4×C61 | C2×C16 | semidirect |
| 83. D244 | C2×C16 | semidirect |
| 91. #92418 | C2×C16 | semidirect |
| 136. C61 | #12062 | semidirect |
| 190. D4 | D61⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462198 | 2 |
| D4×#11758187 | 2 |
| #21460842 | 2 |
| #21460770 | 2 |
| D4⋊#11758187 | 2 |
| #21460734 | 2 |
| #21444611 | 2 |
| #12062 | 61 |