Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
296 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21426333 | C2 | semidirect |
| 3. #21426234 | C2 | semidirect |
| 4. #21423624 | C2 | semidirect |
| 5. #21422140 | C2 | semidirect |
| 6. #21422064 | C2 | semidirect |
| 7. C59×#1338 | C2 | semidirect |
| 147. #1338 | D59 | semidirect |
| 173. C59 | #12388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437186 | 2 |
| #21426333 | 2 |
| #21426234 | 2 |
| #21423624 | 2 |
| #21422140 | 2 |
| #21422064 | 2 |
| C59×#1338 | 2 |
| #12388 | 59 |