Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
682 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21425036 | C2 | semidirect |
| 3. #21422796 | C2 | semidirect |
| 6. #21422439 | C2 | semidirect |
| 7. C59×#1531 | C2 | semidirect |
| 204. #1531 | D59 | semidirect |
| 237. C59 | #8461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437963 | 2 |
| #21425036 | 2 |
| #21422796 | 2 |
| #21422792 | 2 |
| #21422706 | 2 |
| #21422439 | 2 |
| C59×#1531 | 2 |
| #8461 | 59 |