Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
450 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21422690 | C2 | semidirect |
| 4. #21422607 | C2 | semidirect |
| 5. #21421989 | C2 | semidirect |
| 6. #21421968 | C2 | semidirect |
| 10. #16837697 | C4 | semidirect |
| 11. #16837692 | C4 | semidirect |
| 12. #16837612 | C4 | semidirect |
| 13. #16837607 | C4 | semidirect |
| 227. C59 | #9160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434258 | 2 |
| #21433116 | 2 |
| #21422690 | 2 |
| #21422607 | 2 |
| #21421989 | 2 |
| #21421968 | 2 |
| C59×#1759 | 2 |
| #9160 | 59 |