Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21423689 | C2 | semidirect |
| 3. D8×C59⋊C8 | C2 | semidirect |
| 4. #21422159 | C2 | semidirect |
| 5. #21422151 | C2 | semidirect |
| 6. #21422143 | C2 | semidirect |
| 7. C59×#2224 | C2 | semidirect |
| 52. D8×C59 | SD16 | semidirect |
| 96. C59⋊C8 | D16 | semidirect |
| 112. #2224 | D59 | semidirect |
| 139. C59 | #12416 | semidirect |
| 174. D8 | #11745671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426131 | 2 |
| #21423689 | 2 |
| D8×C59⋊C8 | 2 |
| #21422159 | 2 |
| #21422151 | 2 |
| #21422143 | 2 |
| C59×#2224 | 2 |
| #12416 | 59 |