Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21422647 | C2 | semidirect |
| 5. #21422543 | C2 | semidirect |
| 6. #21421962 | C2 | semidirect |
| 7. C59×#3113 | C2 | semidirect |
| 192. #3113 | D59 | semidirect |
| 228. C59 | #10024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434485 | 2 |
| #21429956 | 2 |
| #21422719 | 2 |
| #21422647 | 2 |
| #21422543 | 2 |
| #21421962 | 2 |
| C59×#3113 | 2 |
| #10024 | 59 |