Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 183 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. #21438870 | C2 | semidirect |
| 2. C2×#16837838 | C2 | semidirect |
| 3. #21426041 | C2 | semidirect |
| 4. #21425831 | C2 | semidirect |
| 5. #21425717 | C2 | semidirect |
| 6. C59×#3058 | C2 | semidirect |
| 12. #16838202 | C22 | semidirect |
| 16. #16837838 | C22 | semidirect |
| 19. C2×#14273667 | C22 | semidirect |
| 20. #16837211 | C22 | semidirect |
| 21. #16837184 | C22 | semidirect |
| 22. C22×D8×C59 | C22 | semidirect |
| 25. C59×#469 | C22 | semidirect |
| 27. C59×#427 | C22 | semidirect |
| 46. #14273749 | D4 | semidirect |
| 49. C2×Dic236 | D4 | semidirect |
| 53. C2×D472 | D4 | semidirect |
| 199. #3058 | D59 | semidirect |
| 217. C22×D8 | C2×D59 | semidirect |
| 225. #469 | C2×D59 | semidirect |
| 227. #427 | C2×D59 | semidirect |
| 231. C59 | #33531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438870 | 2 |
| C2×#16837838 | 2 |
| #21426041 | 2 |
| #21425831 | 2 |
| #21425717 | 2 |
| C59×#3058 | 2 |
| #33531 | 59 |