Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
450 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21424234 | C2 | semidirect |
| 3. #21422780 | C2 | semidirect |
| 4. #21422776 | C2 | semidirect |
| 7. C59×#1450 | C2 | semidirect |
| 150. #1450 | D59 | semidirect |
| 174. C59 | #9769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837749 | 2 |
| #21424234 | 2 |
| #21422780 | 2 |
| #21422776 | 2 |
| #21422763 | 2 |
| C59×#1450 | 2 |
| #9769 | 59 |