Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21426341 | C2 | semidirect |
| 3. #21426143 | C2 | semidirect |
| 4. #21422149 | C2 | semidirect |
| 5. #21422065 | C2 | semidirect |
| 166. C59 | #12351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436670 | 2 |
| #21426341 | 2 |
| #21426143 | 2 |
| #21422149 | 2 |
| #21422065 | 2 |
| #21422054 | 2 |
| C59×#1689 | 2 |
| #12351 | 59 |