Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
392 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21422794 | C2 | semidirect |
| 4. #21422596 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 7. C59×#1573 | C2 | semidirect |
| 180. #1573 | D59 | semidirect |
| 212. C59 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435101 | 2 |
| #21425026 | 2 |
| #21422794 | 2 |
| #21422596 | 2 |
| #21422447 | 2 |
| #21421953 | 2 |
| C59×#1573 | 2 |
| #10510 | 59 |