Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
538 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21422777 | C2 | semidirect |
| 5. #21421998 | C2 | semidirect |
| 6. #21421997 | C2 | semidirect |
| 7. C59×#1548 | C2 | semidirect |
| 169. #1548 | D59 | semidirect |
| 196. C59 | #9391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433119 | 2 |
| #21429270 | 2 |
| #21424085 | 2 |
| #21422777 | 2 |
| #21421998 | 2 |
| #21421997 | 2 |
| C59×#1548 | 2 |
| #9391 | 59 |