Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
532 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 115 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. #101×Dic59 | C2 | semidirect |
| 4. #21422223 | C2 | semidirect |
| 5. C59×#1394 | C2 | semidirect |
| 16. #16837198 | C4 | semidirect |
| 41. #14273646 | C2×C4 | semidirect |
| 50. #101×C59 | C2×C4 | semidirect |
| 154. Dic59 | #355 | semidirect |
| 159. #1394 | D59 | semidirect |
| 180. C59 | C4×#355 | semidirect |
| 208. #101 | C4×D59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426639 | 2 |
| C2×#16837198 | 2 |
| #101×Dic59 | 2 |
| #21422223 | 2 |
| C59×#1394 | 2 |
| C4×#355 | 59 |