Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
764 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 764 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 |
|---|---|---|
| 2. #21432123 | C2 | semidirect |
| 3. #21424014 | C2 | semidirect |
| 4. #21422629 | C2 | semidirect |
| 5. #21422626 | C2 | semidirect |
| 6. #21422005 | C2 | semidirect |
| 7. C59×#3007 | C2 | semidirect |
| 248. #3007 | D59 | semidirect |
| 288. C59 | #9981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433348 | 2 |
| #21432123 | 2 |
| #21424014 | 2 |
| #21422629 | 2 |
| #21422626 | 2 |
| #21422005 | 2 |
| C59×#3007 | 2 |
| #9981 | 59 |