Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
770 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#16837557 | C2 | semidirect |
| 4. #21424030 | C2 | semidirect |
| 6. #21421944 | C2 | semidirect |
| 7. C59×#1996 | C2 | semidirect |
| 226. #1996 | D59 | semidirect |
| 261. C59 | #9956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434849 | 2 |
| C2×#16837557 | 2 |
| #21427754 | 2 |
| #21424030 | 2 |
| #21422663 | 2 |
| #21421944 | 2 |
| C59×#1996 | 2 |
| #9956 | 59 |