Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #21435302 | C2 | semidirect |
| 5. #21422712 | C2 | semidirect |
| 6. #21421996 | C2 | semidirect |
| 7. C59×#1470 | C2 | semidirect |
| 174. #1470 | D59 | semidirect |
| 204. C59 | #10131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435302 | 2 |
| #21435039 | 2 |
| C2×#16837768 | 2 |
| #21422809 | 2 |
| #21422712 | 2 |
| #21421996 | 2 |
| C59×#1470 | 2 |
| #10131 | 59 |