Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×C22⋊(C59⋊C16) | C2 | semidirect |
| 3. #21422107 | C2 | semidirect |
| 4. #21422104 | C2 | semidirect |
| 5. C59×#1807 | C2 | semidirect |
| 6. C2×#14273749 | C4 | semidirect |
| 9. #16837643 | C4 | semidirect |
| 11. #16837638 | C4 | semidirect |
| 15. #16837440 | C4 | semidirect |
| 167. #1807 | D59 | semidirect |
| 194. C59 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433677 | 2 |
| C2×C22⋊(C59⋊C16) | 2 |
| #21422107 | 2 |
| #21422104 | 2 |
| C59×#1807 | 2 |
| #11885 | 59 |