Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
408 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 2. C2×#16840686 | C2 | semidirect |
| 4. #21461924 | C2 | semidirect |
| 5. #21460893 | C2 | semidirect |
| 6. #21460859 | C2 | semidirect |
| 23. #16839566 | C4 | semidirect |
| 24. #16839564 | C4 | semidirect |
| 25. #16839562 | C4 | semidirect |
| 26. C61×#358 | C4 | semidirect |
| 90. Q16×C61 | C4⋊C4 | semidirect |
| 99. D488 | C4⋊C4 | semidirect |
| 186. #358 | #6923 | semidirect |
| 190. C61 | #12955 | semidirect |
| 241. Q16 | C4⋊#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840808 | 2 |
| C2×#16840686 | 2 |
| C2×#16840679 | 2 |
| #21461924 | 2 |
| #21460893 | 2 |
| #21460859 | 2 |
| #21447530 | 2 |
| #12955 | 61 |