Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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×#16837845 | C2 | semidirect |
| 3. #21433751 | C2 | semidirect |
| 4. #21426049 | C2 | semidirect |
| 5. #21425833 | C2 | semidirect |
| 6. C59×#2115 | C2 | semidirect |
| 15. C22×Dic236 | C22 | semidirect |
| 18. #16837845 | C22 | semidirect |
| 21. #16837660 | C22 | semidirect |
| 23. #16837440 | C22 | semidirect |
| 25. #16837213 | C22 | semidirect |
| 27. C2×M32×C59 | C22 | semidirect |
| 28. C59×#349 | C22 | semidirect |
| 198. #2115 | D59 | semidirect |
| 219. C2×M32 | C2×D59 | semidirect |
| 225. #349 | C2×D59 | semidirect |
| 226. C59 | #33532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438870 | 2 |
| C2×#16837845 | 2 |
| #21433751 | 2 |
| #21426049 | 2 |
| #21425833 | 2 |
| C59×#2115 | 2 |
| #33532 | 59 |