Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
204 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 65 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×#16837240 | C2 | semidirect |
| 2. C22×C59⋊C32 | C2 | semidirect |
| 3. #21426187 | C2 | semidirect |
| 4. #21422297 | C2 | semidirect |
| 5. #21422276 | C2 | semidirect |
| 6. #21422274 | C2 | semidirect |
| 28. C59⋊C32 | D4 | semidirect |
| 83. C22×C59 | SD64 | semidirect |
| 116. C59 | #13696 | semidirect |
| 178. C22 | #16837240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837240 | 2 |
| C22×C59⋊C32 | 2 |
| #21426187 | 2 |
| #21422297 | 2 |
| #21422276 | 2 |
| #21422274 | 2 |
| C59×#2215 | 2 |
| #13696 | 59 |