Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
290 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16837235 | C2 | semidirect |
| 3. M64×D59 | C2 | semidirect |
| 4. #21422239 | C2 | semidirect |
| 5. #21422238 | C2 | semidirect |
| 6. #21422237 | C2 | semidirect |
| 7. C59×#1401 | C2 | semidirect |
| 18. #16837236 | C22 | semidirect |
| 22. C2×C59⋊C32 | C22 | semidirect |
| 25. C59×M64 | C22 | semidirect |
| 26. C2×C32×C59 | C22 | semidirect |
| 144. #1401 | D59 | semidirect |
| 166. M64 | C2×D59 | semidirect |
| 169. C2×C32 | C2×D59 | semidirect |
| 170. C59 | #13558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #504×D59 | 2 |
| C2×#16837235 | 2 |
| M64×D59 | 2 |
| #21422239 | 2 |
| #21422238 | 2 |
| #21422237 | 2 |
| C59×#1401 | 2 |
| #13558 | 59 |