Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
724 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 87 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×#16837558 | C2 | semidirect |
| 4. #21422461 | C2 | semidirect |
| 6. #21421983 | C2 | semidirect |
| 7. C59×#1784 | C2 | semidirect |
| 212. #1784 | D59 | semidirect |
| 246. C59 | #9989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434903 | 2 |
| C2×#16837558 | 2 |
| C2×#16837541 | 2 |
| #21422461 | 2 |
| #21422457 | 2 |
| #21421983 | 2 |
| C59×#1784 | 2 |
| #9989 | 59 |