Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
316 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21425891 | C2 | semidirect |
| 5. C4×#14273663 | C2 | semidirect |
| 6. #21422208 | C2 | semidirect |
| 7. C59×#1376 | C2 | semidirect |
| 16. #16837219 | C4 | semidirect |
| 17. #16837216 | C4 | semidirect |
| 143. #1376 | D59 | semidirect |
| 164. C59 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425891 | 2 |
| #21425846 | 2 |
| #21425825 | 2 |
| #21424984 | 2 |
| C4×#14273663 | 2 |
| #21422208 | 2 |
| C59×#1376 | 2 |
| #13137 | 59 |