Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1328 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 279 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. #21432788 | C2 | semidirect |
| 3. #21424514 | C2 | semidirect |
| 4. #21424382 | C2 | semidirect |
| 5. #21424047 | C2 | semidirect |
| 6. #21423896 | C2 | semidirect |
| 7. C59×#3573 | C2 | semidirect |
| 8. C22×C8×D59 | C22 | semidirect |
| 14. #16837430 | C22 | semidirect |
| 18. #16837365 | C22 | semidirect |
| 19. #16837357 | C22 | semidirect |
| 20. #16837173 | C22 | semidirect |
| 57. C2×M16×C59 | D4 | semidirect |
| 60. C22×C8×C59 | D4 | semidirect |
| 141. #3573 | D59 | semidirect |
| 170. C59 | #21483 | semidirect |
| 185. C2×M16 | C22⋊D59 | semidirect |
| 191. C22×C8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433488 | 2 |
| #21432788 | 2 |
| #21424514 | 2 |
| #21424382 | 2 |
| #21424047 | 2 |
| #21423896 | 2 |
| C59×#3573 | 2 |
| #21483 | 59 |