Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
274 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21447859 | C2 | semidirect |
| 3. Q16×#92418 | C2 | semidirect |
| 4. #21443888 | C2 | semidirect |
| 5. #21443866 | C2 | semidirect |
| 6. #21443865 | C2 | semidirect |
| 7. C61×#2207 | C2 | semidirect |
| 54. Q16×C61 | D8 | semidirect |
| 101. #92418 | SD32 | semidirect |
| 118. #2207 | D61 | semidirect |
| 144. C61 | #12425 | semidirect |
| 176. Q16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447859 | 2 |
| #21445433 | 2 |
| Q16×#92418 | 2 |
| #21443888 | 2 |
| #21443866 | 2 |
| #21443865 | 2 |
| C61×#2207 | 2 |
| #12425 | 61 |