Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
11422 conjugacy classes of subgroups; only the 5752 normal subgroups are shown.
This group has 11422 conjugacy classes of subgroups — too many to draw. Only its 5752 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. C22×#14519865 | C2 | direct (N × H) |
| 2. C23×#11758213 | C2 | semidirect |
| 3. C23×D61⋊C8 | C2 | semidirect |
| 5. C2×#14519865 | C22 | direct (N × H) |
| 6. C22×#11758213 | C22 | semidirect |
| 7. C22×D61⋊C8 | C22 | semidirect |
| 15. #14519865 | C23 | direct (N × H) |
| 16. C2×#11758213 | C23 | semidirect |
| 17. C2×D61⋊C8 | C23 | semidirect |
| 43. #11758213 | C24 | semidirect |
| 44. D61⋊C8 | C24 | semidirect |
| 45. C23×C61 | #131 | semidirect |
| 59. C22×C61 | C2×#131 | semidirect |
| 70. C2×C61 | C22×#131 | semidirect |
| 83. C61 | C23×#131 | semidirect |
| 116. C23 | #14519865 | direct (N × H) |
| 129. C22 | C2×#14519865 | direct (N × H) |
| 135. C2 | C22×#14519865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519865 | 2 |
| C23×#11758213 | 2 |
| C23×D61⋊C8 | 2 |
| C23×#11758226 | 2 |
| C23×#131 | 61 |