Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1054 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 10. C4×#11745672 | C4 | semidirect |
| 70. #11745672 | C42 | semidirect |
| 140. C59 | #20507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11745672 | 2 |
| #21426459 | 2 |
| C4×#14273660 | 2 |
| #21423929 | 2 |
| #21423926 | 2 |
| #21423783 | 2 |
| C59×#2276 | 2 |
| #20507 | 59 |