Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
576 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21427208 | C2 | semidirect |
| 3. #21422605 | C2 | semidirect |
| 4. #21421988 | C2 | semidirect |
| 5. C59×#1533 | C2 | semidirect |
| 9. #16837797 | C4 | semidirect |
| 10. #16837792 | C4 | semidirect |
| 34. #14273727 | C2×C4 | semidirect |
| 35. #14273724 | C2×C4 | semidirect |
| 44. #14273638 | C2×C4 | semidirect |
| 167. #1533 | D59 | semidirect |
| 193. C59 | #9441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434560 | 2 |
| #21427208 | 2 |
| #21422605 | 2 |
| #21421988 | 2 |
| C59×#1533 | 2 |
| #9441 | 59 |