Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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. C23×#11758185 | C2 | semidirect |
| 2. C2×#16839569 | C2 | semidirect |
| 3. #21445857 | C2 | semidirect |
| 4. #21443914 | C2 | semidirect |
| 25. C2×#11758185 | D4 | semidirect |
| 124. C22×C61 | #359 | semidirect |
| 158. C61 | #13063 | semidirect |
| 261. C22 | #16839569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11758185 | 2 |
| C2×#16839569 | 2 |
| #21445857 | 2 |
| #21443914 | 2 |
| C61×#3050 | 2 |
| #13063 | 61 |