Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
948 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 114 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×#16840679 | C2 | semidirect |
| 2. #21462047 | C2 | semidirect |
| 3. #21461695 | C2 | semidirect |
| 5. C2×#14519852 | C22 | semidirect |
| 6. C2×#14519845 | C22 | semidirect |
| 16. C2×#14519800 | C4 | semidirect |
| 19. C22×D488 | C4 | semidirect |
| 21. C22×Q16×C61 | C4 | semidirect |
| 98. Q16×C61 | C22⋊C4 | semidirect |
| 109. D488 | C22⋊C4 | semidirect |
| 160. C22×C61 | #360 | semidirect |
| 197. C22×Q16 | #6923 | semidirect |
| 208. C61 | #12735 | semidirect |
| 282. Q16 | C22⋊#6923 | semidirect |
| 357. C22 | #16840679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840679 | 2 |
| #21462047 | 2 |
| #21461695 | 2 |
| C22×#14519800 | 2 |
| #12735 | 61 |