Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21433076 | C2 | semidirect |
| 3. #21422671 | C2 | semidirect |
| 4. #21422513 | C2 | semidirect |
| 5. #21421960 | C2 | semidirect |
| 6. #21421959 | C2 | semidirect |
| 7. C59×#1514 | C2 | semidirect |
| 9. #16837794 | C4 | semidirect |
| 10. #16837789 | C4 | semidirect |
| 11. #16837770 | C4 | semidirect |
| 12. #16837766 | C4 | semidirect |
| 202. #1514 | D59 | semidirect |
| 239. C59 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435133 | 2 |
| #21433076 | 2 |
| #21422671 | 2 |
| #21422513 | 2 |
| #21421960 | 2 |
| #21421959 | 2 |
| C59×#1514 | 2 |
| #9370 | 59 |