Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
178 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21425880 | C2 | semidirect |
| 3. #21422298 | C2 | semidirect |
| 4. #21422296 | C2 | semidirect |
| 5. #21422275 | C2 | semidirect |
| 6. #21422275 | C2 | semidirect |
| 7. C59×C22⋊C32 | C2 | semidirect |
| 89. C22⋊C32 | D59 | semidirect |
| 106. C59 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426182 | 2 |
| #21425880 | 2 |
| #21422298 | 2 |
| #21422296 | 2 |
| #21422275 | 2 |
| C59×C22⋊C32 | 2 |
| #13713 | 59 |