Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C2×#16837235 | C2 | semidirect |
| 2. #21426184 | C2 | semidirect |
| 4. #21422296 | C2 | semidirect |
| 5. #21422277 | C2 | semidirect |
| 6. #21422274 | C2 | semidirect |
| 7. C2×C59×SD64 | C2 | semidirect |
| 39. C32×C59 | D4 | semidirect |
| 91. C2×SD64 | D59 | semidirect |
| 116. C59 | #13699 | semidirect |
| 135. C32 | C22⋊D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837235 | 2 |
| #21426184 | 2 |
| #21426179 | 2 |
| #21422296 | 2 |
| #21422277 | 2 |
| #21422274 | 2 |
| C2×C59×SD64 | 2 |
| #13699 | 59 |