Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 171 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. #21434577 | C2 | semidirect |
| 3. #21432948 | C2 | semidirect |
| 4. #21426149 | C2 | semidirect |
| 5. #21426129 | C2 | semidirect |
| 6. #21425854 | C2 | semidirect |
| 7. #21425812 | C2 | semidirect |
| 8. #21425804 | C2 | semidirect |
| 9. C22×D16×C59 | C2 | semidirect |
| 15. C2×#14273671 | C22 | semidirect |
| 16. C2×#14273668 | C22 | semidirect |
| 19. #16837785 | C22 | semidirect |
| 20. #16837777 | C22 | semidirect |
| 22. D8×Dic59 | C22 | semidirect |
| 26. Dic59⋊C16 | C22 | semidirect |
| 27. #16837207 | C22 | semidirect |
| 28. #16837204 | C22 | semidirect |
| 29. #16837203 | C22 | semidirect |
| 70. C2×D8×C59 | D4 | semidirect |
| 177. C22×D16 | D59 | semidirect |
| 216. C59 | #33585 | semidirect |
| 233. C2×D8 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837838 | 2 |
| #21434577 | 2 |
| #21432948 | 2 |
| #21426149 | 2 |
| #21426129 | 2 |
| #21425854 | 2 |
| #21425812 | 2 |
| #21425804 | 2 |
| C22×D16×C59 | 2 |
| #33585 | 59 |