Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
328 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 328 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×#16837179 | C2 | semidirect |
| 4. #21424835 | C2 | semidirect |
| 5. #21422204 | C2 | semidirect |
| 6. #21422195 | C2 | semidirect |
| 21. C59×#358 | C4 | semidirect |
| 22. C59×#357 | C4 | semidirect |
| 167. #358 | Dic59 | semidirect |
| 168. #357 | Dic59 | semidirect |
| 171. C59 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837212 | 2 |
| C2×#16837179 | 2 |
| #21424990 | 2 |
| #21424835 | 2 |
| #21422204 | 2 |
| #21422195 | 2 |
| C59×#2139 | 2 |
| #13153 | 59 |