Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #21422115 | C2 | semidirect |
| 5. #21422114 | C2 | semidirect |
| 6. #21422113 | C2 | semidirect |
| 7. C59×#1350 | C2 | semidirect |
| 175. #1350 | D59 | semidirect |
| 201. C59 | #11896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D59 | 2 |
| #21425705 | 2 |
| #21424133 | 2 |
| #21422115 | 2 |
| #21422114 | 2 |
| #21422113 | 2 |
| C59×#1350 | 2 |
| #11896 | 59 |