Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
920 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #21434648 | C2 | semidirect |
| 4. #21430046 | C2 | semidirect |
| 6. #21425076 | C2 | semidirect |
| 7. #21424313 | C2 | semidirect |
| 9. C59×#1966 | C2 | semidirect |
| 191. #1966 | D59 | semidirect |
| 225. C59 | #25691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437980 | 2 |
| #21434648 | 2 |
| #21433919 | 2 |
| #21430046 | 2 |
| #21425314 | 2 |
| #21425076 | 2 |
| #21424313 | 2 |
| #21423909 | 2 |
| C59×#1966 | 2 |
| #25691 | 59 |