Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
828 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16839957 | C2 | semidirect |
| 2. #21446624 | C2 | semidirect |
| 3. C2×D4⋊#92418 | C2 | semidirect |
| 4. #21443702 | C2 | semidirect |
| 5. C61×#2537 | C2 | semidirect |
| 29. #14519774 | D4 | semidirect |
| 31. C4⋊#92418 | D4 | semidirect |
| 60. C2×D4×C61 | D8 | semidirect |
| 171. #2537 | D61 | semidirect |
| 196. C61 | #10228 | semidirect |
| 247. C2×D4 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839957 | 2 |
| #21446624 | 2 |
| C2×D4⋊#92418 | 2 |
| #21443702 | 2 |
| C61×#2537 | 2 |
| #10228 | 61 |