Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #21424318 | C2 | semidirect |
| 5. #21424315 | C2 | semidirect |
| 6. #21422224 | C2 | semidirect |
| 7. C59×#1395 | C2 | semidirect |
| 21. #16837200 | C4 | semidirect |
| 22. #16837198 | C4 | semidirect |
| 188. #1395 | D59 | semidirect |
| 216. C59 | #12975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433160 | 2 |
| #21425779 | 2 |
| #21424477 | 2 |
| #21424318 | 2 |
| #21424315 | 2 |
| #21422224 | 2 |
| C59×#1395 | 2 |
| #12975 | 59 |