Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
380 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21422203 | C2 | semidirect |
| 4. #21422197 | C2 | semidirect |
| 15. C59×#427 | C4 | semidirect |
| 17. C2×#106×C59 | C4 | semidirect |
| 129. #427 | Dic59 | semidirect |
| 131. C2×#106 | Dic59 | semidirect |
| 136. C59 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425717 | 2 |
| #21424142 | 2 |
| #21422203 | 2 |
| #21422197 | 2 |
| C59×#2912 | 2 |
| #12873 | 59 |