Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
258 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 88 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. #21460849 | C2 | semidirect |
| 4. #21460770 | C2 | semidirect |
| 5. D4⋊#11758187 | C2 | semidirect |
| 6. C8×#11758187 | C2 | semidirect |
| 54. #11758199 | C16 | semidirect |
| 70. #11758187 | D8 | semidirect |
| 74. D4×C61 | C2×C16 | semidirect |
| 83. D244 | C2×C16 | semidirect |
| 91. #92418 | C2×C16 | semidirect |
| 136. C61 | C16×D8 | 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 |
| #21460849 | 2 |
| #21460770 | 2 |
| D4⋊#11758187 | 2 |
| C8×#11758187 | 2 |
| #21444611 | 2 |
| C16×D8 | 61 |