Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
6020 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 6020 conjugacy classes of subgroups — too many to draw. Only its 387 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. C2×#16837536 | C2 | semidirect |
| 2. #21432378 | C2 | semidirect |
| 3. #21424027 | C2 | semidirect |
| 4. #21424006 | C2 | semidirect |
| 5. C24×D4×C59 | C2 | semidirect |
| 6. C22×#11745669 | C22 | semidirect |
| 7. C2×#14273701 | C22 | semidirect |
| 10. C2×#14273648 | C22 | semidirect |
| 11. C2×C22⋊(C59⋊C8) | C22 | semidirect |
| 13. #16837262 | C22 | semidirect |
| 19. C22×D236 | C23 | semidirect |
| 22. C22×C59⋊C8 | C23 | semidirect |
| 25. C2×C4⋊Dic59 | C23 | semidirect |
| 42. C22×D4×C59 | D4 | semidirect |
| 58. C24×C59 | D8 | semidirect |
| 108. D4×C59 | #120 | semidirect |
| 130. C22×C59 | #447 | semidirect |
| 140. C24×D4 | D59 | semidirect |
| 164. C59 | #32878 | semidirect |
| 178. C22×D4 | C22⋊D59 | semidirect |
| 205. C24 | #11745669 | semidirect |
| 256. D4 | #14273696 | semidirect |
| 278. C22 | #16837536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837536 | 2 |
| #21432378 | 2 |
| #21424027 | 2 |
| #21424006 | 2 |
| C24×D4×C59 | 2 |
| #32878 | 59 |