Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
516 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21432948 | C2 | semidirect |
| 3. #21425813 | C2 | semidirect |
| 4. #21425004 | C2 | semidirect |
| 5. #21422193 | C2 | semidirect |
| 6. #21422186 | C2 | semidirect |
| 7. C2×C59×#361 | C2 | semidirect |
| 12. C2×#14273668 | C4 | semidirect |
| 32. C2×D472 | C2×C4 | semidirect |
| 42. C2×C59⋊C16 | C2×C4 | semidirect |
| 162. C2×#361 | D59 | semidirect |
| 191. C59 | #13017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273668 | 2 |
| #21432948 | 2 |
| #21425813 | 2 |
| #21425004 | 2 |
| #21422193 | 2 |
| #21422186 | 2 |
| C2×C59×#361 | 2 |
| #13017 | 59 |