Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21425833 | C2 | semidirect |
| 3. #21425801 | C2 | semidirect |
| 4. C2×#16837187 | C2 | semidirect |
| 5. #21424139 | C2 | semidirect |
| 6. #21422193 | C2 | semidirect |
| 7. C59×#2155 | C2 | semidirect |
| 171. #2155 | D59 | semidirect |
| 202. C59 | #13401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433817 | 2 |
| #21425833 | 2 |
| #21425801 | 2 |
| C2×#16837187 | 2 |
| #21424139 | 2 |
| #21422193 | 2 |
| C59×#2155 | 2 |
| #13401 | 59 |