Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21422107 | C2 | semidirect |
| 5. C22×Dic236 | C4 | semidirect |
| 10. #16837643 | C4 | semidirect |
| 12. C2×#14273661 | C4 | semidirect |
| 169. C59 | #11887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837643 | 2 |
| C2×C22⋊(C59⋊C16) | 2 |
| #21422107 | 2 |
| C59×#1808 | 2 |
| #11887 | 59 |