Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
558 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 558 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. #21422769 | C2 | semidirect |
| 5. #21422767 | C2 | semidirect |
| 6. #21421999 | C2 | semidirect |
| 7. C59×#1303 | C2 | semidirect |
| 179. #1303 | D59 | semidirect |
| 204. C59 | #9393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433119 | 2 |
| #21429091 | 2 |
| #21424085 | 2 |
| #21422769 | 2 |
| #21422767 | 2 |
| #21421999 | 2 |
| C59×#1303 | 2 |
| #9393 | 59 |