Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
350 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16837179 | C2 | semidirect |
| 5. #21424847 | C2 | semidirect |
| 6. #21422203 | C2 | semidirect |
| 7. C59×#1383 | C2 | semidirect |
| 16. #16837204 | C4 | semidirect |
| 138. #1383 | D59 | semidirect |
| 158. C59 | #13155 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837214 | 2 |
| #21425813 | 2 |
| C2×#16837179 | 2 |
| #21424970 | 2 |
| #21424847 | 2 |
| #21422203 | 2 |
| C59×#1383 | 2 |
| #13155 | 59 |