Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 251 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. #21443736 | C2 | semidirect |
| 3. C8×#11758185 | C2 | semidirect |
| 13. #14519717 | C8 | direct (N × H) |
| 35. #11758185 | C2×C8 | semidirect |
| 45. C8×C61 | M32 | semidirect |
| 70. C61 | C8×M32 | semidirect |
| 103. C8 | #14519717 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519717 | 2 |
| #21443736 | 2 |
| C8×#11758185 | 2 |
| C2×C82×C61 | 2 |
| C8×M32 | 61 |