Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21426313 | C2 | semidirect |
| 3. #21426269 | C2 | semidirect |
| 4. #21426174 | C2 | semidirect |
| 6. #21425985 | C2 | semidirect |
| 7. #21425912 | C2 | semidirect |
| 8. C59×#3177 | C2 | semidirect |
| 18. #16837224 | C22 | semidirect |
| 19. #16837223 | C22 | semidirect |
| 20. #16837218 | C22 | semidirect |
| 23. #16837180 | C22 | semidirect |
| 25. C59×#499 | C22 | semidirect |
| 26. C59×#494 | C22 | semidirect |
| 30. C59×#441 | C22 | semidirect |
| 157. #3177 | D59 | semidirect |
| 173. #499 | C2×D59 | semidirect |
| 174. #494 | C2×D59 | semidirect |
| 182. #441 | C2×D59 | semidirect |
| 193. C59 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433000 | 2 |
| #21426313 | 2 |
| #21426269 | 2 |
| #21426174 | 2 |
| #21426046 | 2 |
| #21425985 | 2 |
| #21425912 | 2 |
| C59×#3177 | 2 |
| #33693 | 59 |