Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
396 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 102 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×#16840687 | C2 | semidirect |
| 2. C2×#16840686 | C2 | semidirect |
| 5. #21460884 | C2 | semidirect |
| 6. #21460884 | C2 | semidirect |
| 19. C2×#14519717 | C4 | semidirect |
| 24. C2×C16×D61 | C4 | semidirect |
| 25. C2×C16×D61 | C4 | semidirect |
| 26. C2×M32×C61 | C4 | semidirect |
| 109. C16×C61 | C22⋊C4 | semidirect |
| 111. #11758185 | C22⋊C4 | semidirect |
| 162. C2×D61 | #365 | semidirect |
| 193. C2×M32 | #6923 | semidirect |
| 206. C61 | #12831 | semidirect |
| 291. C16 | C22⋊#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840687 | 2 |
| C2×#16840686 | 2 |
| #21461698 | 2 |
| #21461695 | 2 |
| #21460884 | 2 |
| C2×M32×D61 | 2 |
| #12831 | 61 |