Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 508 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. C2×#16840809 | C2 | semidirect |
| 2. C2×#16840680 | C2 | semidirect |
| 3. C2×#16840678 | C2 | semidirect |
| 4. #21461968 | C2 | semidirect |
| 5. #21460884 | C2 | semidirect |
| 6. #21460859 | C2 | semidirect |
| 24. C2×#14519722 | C4 | semidirect |
| 25. C2×#14519721 | C4 | semidirect |
| 26. C2×#14519718 | C4 | semidirect |
| 28. C2×D16×C61 | C4 | semidirect |
| 111. D8×C61 | C22⋊C4 | semidirect |
| 119. Dic244 | C22⋊C4 | semidirect |
| 221. C2×D16 | #6923 | semidirect |
| 234. C61 | #13040 | semidirect |
| 311. D8 | C22⋊#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840809 | 2 |
| C2×#16840680 | 2 |
| C2×#16840678 | 2 |
| #21461968 | 2 |
| #21460884 | 2 |
| #21460859 | 2 |
| C2×#16840196 | 2 |
| #13040 | 61 |