Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 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. #21433226 | C2 | semidirect |
| 3. C4×#14273655 | C2 | semidirect |
| 4. #21422513 | C2 | semidirect |
| 5. #21421985 | C2 | semidirect |
| 6. #21421929 | C2 | semidirect |
| 7. C59×#1962 | C2 | semidirect |
| 10. #16837694 | C4 | semidirect |
| 11. #16837689 | C4 | semidirect |
| 12. #16837599 | C4 | semidirect |
| 13. #16837594 | C4 | semidirect |
| 179. Dic118 | #104 | semidirect |
| 213. #1962 | D59 | semidirect |
| 249. C59 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434150 | 2 |
| #21433226 | 2 |
| C4×#14273655 | 2 |
| #21422513 | 2 |
| #21421985 | 2 |
| #21421929 | 2 |
| C59×#1962 | 2 |
| #8970 | 59 |