Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
298 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 61 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. #21426342 | C2 | semidirect |
| 3. #21426141 | C2 | semidirect |
| 4. #21423586 | C2 | semidirect |
| 5. #21422149 | C2 | semidirect |
| 6. #21422055 | C2 | semidirect |
| 7. C59×#1333 | C2 | semidirect |
| 146. #1333 | D59 | semidirect |
| 172. C59 | #12350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436703 | 2 |
| #21426342 | 2 |
| #21426141 | 2 |
| #21423586 | 2 |
| #21422149 | 2 |
| #21422055 | 2 |
| C59×#1333 | 2 |
| #12350 | 59 |