Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21424140 | C2 | semidirect |
| 4. #21422217 | C2 | semidirect |
| 5. C59×#1391 | C2 | semidirect |
| 6. C2×#14273735 | C4 | semidirect |
| 12. #16837425 | C4 | semidirect |
| 14. #16837368 | C4 | semidirect |
| 15. C2×C8×Dic59 | C4 | semidirect |
| 150. #1391 | D59 | semidirect |
| 171. C59 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432804 | 2 |
| #21425759 | 2 |
| #21424140 | 2 |
| #21422217 | 2 |
| C59×#1391 | 2 |
| #12807 | 59 |