Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 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×#16837838 | C2 | semidirect |
| 2. #21433677 | C2 | semidirect |
| 3. #21426025 | C2 | semidirect |
| 4. #21426008 | C2 | semidirect |
| 5. #21425812 | C2 | semidirect |
| 6. #21425707 | C2 | semidirect |
| 7. C23×D8×C59 | C2 | semidirect |
| 8. C2×#14273749 | C22 | semidirect |
| 11. C2×#14273671 | C22 | semidirect |
| 12. C2×#14273668 | C22 | semidirect |
| 13. C2×#14273667 | C22 | semidirect |
| 14. #16837643 | C22 | semidirect |
| 15. #16837638 | C22 | semidirect |
| 17. #16837440 | C22 | semidirect |
| 19. #16837203 | C22 | semidirect |
| 20. C22⋊(C59⋊C16) | C22 | semidirect |
| 30. C2×Dic236 | C23 | semidirect |
| 32. C2×D472 | C23 | semidirect |
| 42. C2×C59⋊C16 | C23 | semidirect |
| 43. #14273661 | C23 | semidirect |
| 61. C2×D8×C59 | D4 | semidirect |
| 163. C22×C59 | #509 | semidirect |
| 173. C23×D8 | D59 | semidirect |
| 206. C59 | #33517 | semidirect |
| 226. C2×D8 | C22⋊D59 | semidirect |
| 343. C22 | #16837838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837838 | 2 |
| #21433677 | 2 |
| #21426025 | 2 |
| #21426008 | 2 |
| #21425812 | 2 |
| #21425707 | 2 |
| C23×D8×C59 | 2 |
| #33517 | 59 |