Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
244 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 80 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. #21462205 | C2 | semidirect |
| 2. D4×#11758187 | C2 | semidirect |
| 3. #21460849 | C2 | semidirect |
| 4. #21460770 | C2 | semidirect |
| 5. D4⋊#11758187 | C2 | semidirect |
| 6. #21460731 | C2 | semidirect |
| 70. #11758187 | D8 | semidirect |
| 74. D4×C61 | M32 | semidirect |
| 136. C61 | #12038 | semidirect |
| 190. D4 | #14519852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462205 | 2 |
| D4×#11758187 | 2 |
| #21460849 | 2 |
| #21460770 | 2 |
| D4⋊#11758187 | 2 |
| #21460731 | 2 |
| #21444611 | 2 |
| #12038 | 61 |