Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
584 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 7. #16837197 | C4 | direct (N × H) |
| 10. C2×C4×Q8×C59 | C4 | semidirect |
| 12. C59×#391 | C4 | semidirect |
| 15. C59×#382 | C4 | semidirect |
| 17. C43×C59 | C4 | semidirect |
| 50. C2×Q8×C59 | C42 | semidirect |
| 81. C42×C59 | C42 | semidirect |
| 142. C4×C59 | #354 | semidirect |
| 155. C2×C4×Q8 | Dic59 | semidirect |
| 158. #391 | Dic59 | semidirect |
| 161. #382 | Dic59 | semidirect |
| 164. C43 | Dic59 | semidirect |
| 167. C59 | C4×#354 | semidirect |
| 200. C2×Q8 | C4×Dic59 | semidirect |
| 234. C42 | C4×Dic59 | semidirect |
| 292. C4 | #16837197 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837197 | 2 |
| C4×#14273642 | 2 |
| #21422221 | 2 |
| C4×#124×C59 | 2 |
| C4×#354 | 59 |