Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
526 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21425070 | C2 | semidirect |
| 4. C2×#16837144 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C2×C59×#491 | C2 | semidirect |
| 183. C2×#491 | D59 | semidirect |
| 219. C59 | #10083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837764 | 2 |
| #21432146 | 2 |
| #21425070 | 2 |
| C2×#16837144 | 2 |
| C2×#16837141 | 2 |
| #21421978 | 2 |
| C2×C59×#491 | 2 |
| #10083 | 59 |