Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21434585 | C2 | semidirect |
| 3. C2×#16837218 | C2 | semidirect |
| 4. C2×#16837210 | C2 | semidirect |
| 5. #21425007 | C2 | semidirect |
| 6. #21422184 | C2 | semidirect |
| 7. C22×SD32×C59 | C2 | semidirect |
| 196. C22×SD32 | D59 | semidirect |
| 231. C59 | #13337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837838 | 2 |
| #21434585 | 2 |
| C2×#16837218 | 2 |
| C2×#16837210 | 2 |
| #21425007 | 2 |
| #21422184 | 2 |
| C22×SD32×C59 | 2 |
| #13337 | 59 |