Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
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×#17986747 | C2 | semidirect |
| 2. C2×#17986386 | C2 | semidirect |
| 3. #22587632 | C2 | direct (N × H) |
| 4. C2×#17985741 | C2 | semidirect |
| 5. C2×#17985738 | C2 | semidirect |
| 6. C2×#490×C71 | C2 | semidirect |
| 11. #17986747 | C22 | semidirect |
| 17. #17986386 | C22 | semidirect |
| 19. #17985741 | C22 | semidirect |
| 20. #17985738 | C22 | semidirect |
| 24. #490×C71 | C22 | semidirect |
| 158. C2×C71 | #1656 | semidirect |
| 164. C2×#490 | D71 | semidirect |
| 168. C71 | C2×#1656 | semidirect |
| 183. #490 | C2×D71 | semidirect |
| 320. C2 | #22587632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986747 | 2 |
| C2×#17986386 | 2 |
| #22587632 | 2 |
| C2×#17985741 | 2 |
| C2×#17985738 | 2 |
| C2×#490×C71 | 2 |
| C2×#1656 | 71 |