Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 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×#16837843 | C2 | semidirect |
| 3. #21432964 | C2 | semidirect |
| 4. #21426156 | C2 | semidirect |
| 5. #21426134 | C2 | semidirect |
| 6. #21425854 | C2 | semidirect |
| 7. #21425812 | C2 | semidirect |
| 8. #21425804 | C2 | semidirect |
| 9. C22×SD32×C59 | C2 | semidirect |
| 15. C2×#14273673 | C22 | semidirect |
| 16. C2×#14273670 | C22 | semidirect |
| 22. Q16×Dic59 | C22 | semidirect |
| 26. Dic59⋊C16 | C22 | semidirect |
| 27. #16837207 | C22 | semidirect |
| 28. #16837204 | C22 | semidirect |
| 67. C2×Q16×C59 | D4 | semidirect |
| 173. C22×SD32 | D59 | semidirect |
| 211. C59 | #33587 | semidirect |
| 221. C2×Q16 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837843 | 2 |
| #21434577 | 2 |
| #21432964 | 2 |
| #21426156 | 2 |
| #21426134 | 2 |
| #21425854 | 2 |
| #21425812 | 2 |
| #21425804 | 2 |
| C22×SD32×C59 | 2 |
| #33587 | 59 |