Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21434755 | C2 | semidirect |
| 2. #21426315 | C2 | semidirect |
| 3. #21426272 | C2 | semidirect |
| 4. #21426177 | C2 | semidirect |
| 6. #21425987 | C2 | semidirect |
| 7. #21425912 | C2 | semidirect |
| 11. #16837804 | C22 | semidirect |
| 12. #16837782 | C22 | semidirect |
| 16. #16837510 | C22 | semidirect |
| 18. #16837226 | C22 | semidirect |
| 19. #16837223 | C22 | semidirect |
| 20. #16837217 | C22 | semidirect |
| 23. #16837180 | C22 | semidirect |
| 193. C59 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434755 | 2 |
| #21426315 | 2 |
| #21426272 | 2 |
| #21426177 | 2 |
| #21426047 | 2 |
| #21425987 | 2 |
| #21425912 | 2 |
| C59×#2955 | 2 |
| #33693 | 59 |