Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
408 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. C2×#16837217 | C2 | semidirect |
| 4. C2×#16837179 | C2 | semidirect |
| 6. #21424965 | C2 | semidirect |
| 7. C2×C59×#365 | C2 | semidirect |
| 12. C2×Dic472 | C4 | semidirect |
| 13. C2×#14273672 | C4 | semidirect |
| 161. C2×#365 | D59 | semidirect |
| 191. C59 | #13250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837845 | 2 |
| C2×#16837217 | 2 |
| C2×#16837211 | 2 |
| C2×#16837179 | 2 |
| #21424987 | 2 |
| #21424965 | 2 |
| C2×C59×#365 | 2 |
| #13250 | 59 |