Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #21433193 | C2 | semidirect |
| 3. #21422794 | C2 | semidirect |
| 6. #21421957 | C2 | semidirect |
| 7. C59×#1290 | C2 | semidirect |
| 160. #1290 | D59 | semidirect |
| 188. C59 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435296 | 2 |
| #21433193 | 2 |
| #21422794 | 2 |
| #21422730 | 2 |
| #21422494 | 2 |
| #21421957 | 2 |
| C59×#1290 | 2 |
| #9372 | 59 |