Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
324 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16837177 | C2 | semidirect |
| 4. #21424845 | C2 | semidirect |
| 5. #21422191 | C2 | semidirect |
| 6. #21422190 | C2 | semidirect |
| 21. C59×#358 | C4 | semidirect |
| 22. C59×#357 | C4 | semidirect |
| 156. #358 | Dic59 | semidirect |
| 157. #357 | Dic59 | semidirect |
| 160. C59 | #13152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837209 | 2 |
| C2×#16837177 | 2 |
| #21424985 | 2 |
| #21424845 | 2 |
| #21422191 | 2 |
| #21422190 | 2 |
| C59×#2138 | 2 |
| #13152 | 59 |