Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
984 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 203 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. #21423137 | C2 | direct (N × H) |
| 189. C2×C59 | #1617 | semidirect |
| 215. C59 | C2×#1617 | semidirect |
| 369. C2 | #21423137 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838033 | 2 |
| C2×#16837737 | 2 |
| #21423137 | 2 |
| C2×#16837138 | 2 |
| C2×#16837128 | 2 |
| C2×C59×#400 | 2 |
| C2×#1617 | 59 |