Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21422699 | C2 | semidirect |
| 5. #21422453 | C2 | semidirect |
| 6. #21421985 | C2 | semidirect |
| 7. C59×#1307 | C2 | semidirect |
| 186. #1307 | D59 | semidirect |
| 218. C59 | #9351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433919 | 2 |
| #21433108 | 2 |
| #21422699 | 2 |
| #21422528 | 2 |
| #21422453 | 2 |
| #21421985 | 2 |
| C59×#1307 | 2 |
| #9351 | 59 |