Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
902 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 902 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#16837139 | C2 | semidirect |
| 4. #21421974 | C2 | semidirect |
| 14. C2×C22⋊Q8×C59 | C4 | semidirect |
| 18. C59×#380 | C4 | semidirect |
| 193. C2×C22⋊Q8 | Dic59 | semidirect |
| 201. #380 | Dic59 | semidirect |
| 207. C59 | #9154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837265 | 2 |
| #21424006 | 2 |
| C2×#16837139 | 2 |
| #21421974 | 2 |
| C59×#2848 | 2 |
| #9154 | 59 |