Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16837219 | C2 | semidirect |
| 4. C2×#16837205 | C2 | semidirect |
| 6. #21422189 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 17. #16837678 | C4 | semidirect |
| 170. #1387 | D59 | semidirect |
| 198. C59 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837820 | 2 |
| C2×#16837678 | 2 |
| C2×#16837219 | 2 |
| C2×#16837205 | 2 |
| #21424161 | 2 |
| #21422189 | 2 |
| C59×#1387 | 2 |
| #13072 | 59 |