Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
538 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 119 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×#16837215 | C2 | semidirect |
| 3. C2×#16837211 | C2 | semidirect |
| 4. #21424989 | C2 | semidirect |
| 5. #21422194 | C2 | semidirect |
| 6. #21422176 | C2 | semidirect |
| 7. C2×C59×#442 | C2 | semidirect |
| 11. C2×#14273671 | C4 | semidirect |
| 12. C2×#14273668 | C4 | semidirect |
| 32. C2×Dic236 | C2×C4 | semidirect |
| 34. C2×D472 | C2×C4 | semidirect |
| 43. C2×C59⋊C16 | C2×C4 | semidirect |
| 174. C2×#442 | D59 | semidirect |
| 205. C59 | #13037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837838 | 2 |
| C2×#16837215 | 2 |
| C2×#16837211 | 2 |
| #21424989 | 2 |
| #21422194 | 2 |
| #21422176 | 2 |
| C2×C59×#442 | 2 |
| #13037 | 59 |