Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #21425765 | C2 | semidirect |
| 3. #21422272 | C2 | semidirect |
| 4. #21422254 | C2 | semidirect |
| 5. C59×#2134 | C2 | semidirect |
| 6. #16838007 | C4 | semidirect |
| 8. #16837778 | C4 | semidirect |
| 9. #16837766 | C4 | semidirect |
| 15. #16837463 | C4 | semidirect |
| 27. #14273724 | C2×C4 | semidirect |
| 28. #14273719 | C2×C4 | semidirect |
| 42. #14273638 | C2×C4 | semidirect |
| 43. C4×C59⋊C8 | C2×C4 | semidirect |
| 153. #2134 | D59 | semidirect |
| 181. C59 | #13605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435146 | 2 |
| #21425765 | 2 |
| #21422272 | 2 |
| #21422254 | 2 |
| C59×#2134 | 2 |
| #13605 | 59 |