Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21425885 | C2 | semidirect |
| 2. C2×#16837223 | C2 | semidirect |
| 6. #21422206 | C2 | semidirect |
| 7. C59×#1945 | C2 | semidirect |
| 146. #1945 | D59 | semidirect |
| 171. C59 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425885 | 2 |
| C2×#16837223 | 2 |
| C2×#16837214 | 2 |
| #21425811 | 2 |
| #21424962 | 2 |
| #21422206 | 2 |
| C59×#1945 | 2 |
| #13478 | 59 |