Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1138 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C2×#16838150 | C2 | semidirect |
| 2. C2×#16837789 | C2 | semidirect |
| 3. #21423388 | C2 | direct (N × H) |
| 4. C2×#16837144 | C2 | semidirect |
| 5. C2×#16837141 | C2 | semidirect |
| 6. C2×C59×#490 | C2 | semidirect |
| 11. #16838150 | C22 | semidirect |
| 17. #16837789 | C22 | semidirect |
| 19. #16837144 | C22 | semidirect |
| 20. #16837141 | C22 | semidirect |
| 24. C59×#490 | C22 | semidirect |
| 159. C2×#490 | D59 | semidirect |
| 164. C2×C59 | #1656 | semidirect |
| 182. #490 | C2×D59 | semidirect |
| 188. C59 | C2×#1656 | semidirect |
| 320. C2 | #21423388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16838150 | 2 |
| C2×#16837789 | 2 |
| #21423388 | 2 |
| C2×#16837144 | 2 |
| C2×#16837141 | 2 |
| C2×C59×#490 | 2 |
| C2×#1656 | 59 |