Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 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. #21426343 | C2 | semidirect |
| 4. #21422163 | C2 | semidirect |
| 5. #21422157 | C2 | semidirect |
| 6. #21422134 | C2 | semidirect |
| 115. C59 | #12466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426343 | 2 |
| #21426177 | 2 |
| #21425938 | 2 |
| #21422163 | 2 |
| #21422157 | 2 |
| #21422134 | 2 |
| C59×#2231 | 2 |
| #12466 | 59 |