Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
560 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #21425049 | C2 | semidirect |
| 4. #21425041 | C2 | semidirect |
| 6. #21421945 | C2 | semidirect |
| 7. C59×#3229 | C2 | semidirect |
| 124. #11745664 | SD16 | semidirect |
| 188. #3229 | D59 | semidirect |
| 223. C59 | #10206 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435408 | 2 |
| #21434553 | 2 |
| #21425049 | 2 |
| #21425041 | 2 |
| #21422592 | 2 |
| #21421945 | 2 |
| C59×#3229 | 2 |
| #10206 | 59 |