Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
602 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21424936 | C2 | semidirect |
| 3. #21422851 | C2 | semidirect |
| 4. #21422765 | C2 | semidirect |
| 5. #21422764 | C2 | semidirect |
| 6. #21422383 | C2 | semidirect |
| 7. C59×#1965 | C2 | semidirect |
| 142. C59⋊C8 | #100 | semidirect |
| 165. #1965 | D59 | semidirect |
| 194. C59 | #9811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837778 | 2 |
| #21424936 | 2 |
| #21422851 | 2 |
| #21422765 | 2 |
| #21422764 | 2 |
| #21422383 | 2 |
| C59×#1965 | 2 |
| #9811 | 59 |