Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21425085 | C2 | semidirect |
| 4. #21422812 | C2 | semidirect |
| 6. #21422006 | C2 | semidirect |
| 7. C59×#1291 | C2 | semidirect |
| 180. #1291 | D59 | semidirect |
| 211. C59 | #9338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435319 | 2 |
| #21433268 | 2 |
| #21425085 | 2 |
| #21422812 | 2 |
| #21422701 | 2 |
| #21422006 | 2 |
| C59×#1291 | 2 |
| #9338 | 59 |