Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
786 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C4×#14273642 | C2 | semidirect |
| 2. #21422437 | C2 | semidirect |
| 3. #21422093 | C2 | semidirect |
| 8. #16837169 | C22 | semidirect |
| 10. #16837126 | C22 | semidirect |
| 11. C23×D4×C59 | C4 | semidirect |
| 15. C59×#394 | C4 | semidirect |
| 18. C59×#380 | C4 | semidirect |
| 197. C23×D4 | Dic59 | semidirect |
| 203. #394 | Dic59 | semidirect |
| 206. #380 | Dic59 | semidirect |
| 212. C59 | #11772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14273642 | 2 |
| #21422437 | 2 |
| #21422093 | 2 |
| C59×#2408 | 2 |
| #11772 | 59 |