Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #21421943 | C2 | semidirect |
| 4. #21421942 | C2 | semidirect |
| 213. C59 | #8736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426694 | 2 |
| C2×#16837126 | 2 |
| #21421943 | 2 |
| #21421942 | 2 |
| C2×C59×#323 | 2 |
| #8736 | 59 |