Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21433158 | C2 | semidirect |
| 3. #21422624 | C2 | semidirect |
| 4. #21422455 | C2 | semidirect |
| 5. #21422004 | C2 | semidirect |
| 6. #21421973 | C2 | semidirect |
| 7. C59×#1516 | C2 | semidirect |
| 9. #16837730 | C4 | semidirect |
| 11. #16837713 | C4 | semidirect |
| 14. #16837552 | C4 | semidirect |
| 16. #16837535 | C4 | semidirect |
| 220. #1516 | D59 | semidirect |
| 260. C59 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434906 | 2 |
| #21433158 | 2 |
| #21422624 | 2 |
| #21422455 | 2 |
| #21422004 | 2 |
| #21421973 | 2 |
| C59×#1516 | 2 |
| #9332 | 59 |