Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
462 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 13. #16837780 | C4 | semidirect |
| 186. C59 | #13262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837780 | 2 |
| C2×#16837222 | 2 |
| C2×#16837217 | 2 |
| #21425817 | 2 |
| #21425816 | 2 |
| #21423978 | 2 |
| C2×C59×#362 | 2 |
| #13262 | 59 |