Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 2. #21433110 | C2 | semidirect |
| 3. #21422687 | C2 | semidirect |
| 4. #21422603 | C2 | semidirect |
| 5. #21421989 | C2 | semidirect |
| 6. #21421968 | C2 | semidirect |
| 7. C59×#1759 | C2 | semidirect |
| 10. #16837687 | C4 | semidirect |
| 11. #16837682 | C4 | semidirect |
| 12. #16837602 | C4 | semidirect |
| 13. #16837597 | C4 | semidirect |
| 199. #1759 | D59 | semidirect |
| 235. C59 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434247 | 2 |
| #21433110 | 2 |
| #21422687 | 2 |
| #21422603 | 2 |
| #21421989 | 2 |
| #21421968 | 2 |
| C59×#1759 | 2 |
| #9161 | 59 |