Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 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. #21424384 | C2 | semidirect |
| 5. #21424381 | C2 | semidirect |
| 6. #21422216 | C2 | semidirect |
| 7. C59×#1391 | C2 | semidirect |
| 21. #16837196 | C4 | semidirect |
| 22. #16837194 | C4 | semidirect |
| 190. #1391 | D59 | semidirect |
| 218. C59 | #12968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433160 | 2 |
| #21425759 | 2 |
| #21424477 | 2 |
| #21424384 | 2 |
| #21424381 | 2 |
| #21422216 | 2 |
| C59×#1391 | 2 |
| #12968 | 59 |