Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #21424311 | C2 | semidirect |
| 5. #21422223 | C2 | semidirect |
| 6. #21422222 | C2 | semidirect |
| 7. C59×#1857 | C2 | semidirect |
| 20. #16837198 | C4 | semidirect |
| 53. #14273646 | C2×C4 | semidirect |
| 70. #101×C59 | C2×C4 | semidirect |
| 206. #1857 | D59 | semidirect |
| 235. C59 | #12972 | semidirect |
| 274. #101 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427207 | 2 |
| C2×#16837198 | 2 |
| #21424499 | 2 |
| #21424311 | 2 |
| #21422223 | 2 |
| #21422222 | 2 |
| C59×#1857 | 2 |
| #12972 | 59 |