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×#17986388 | C2 | semidirect |
| 3. C2×#17986365 | C2 | semidirect |
| 4. #22587635 | C2 | direct (N × H) |
| 5. C2×#17985738 | C2 | semidirect |
| 6. C2×#330×C71 | C2 | semidirect |
| 11. #17986747 | C22 | semidirect |
| 18. #17986388 | C22 | semidirect |
| 20. #17986365 | C22 | semidirect |
| 23. #17985738 | C22 | semidirect |
| 26. #330×C71 | C22 | semidirect |
| 157. C2×C71 | #1656 | semidirect |
| 166. C2×#330 | D71 | semidirect |
| 168. C71 | C2×#1656 | semidirect |
| 187. #330 | C2×D71 | semidirect |
| 320. C2 | #22587635 | 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×#17986388 | 2 |
| C2×#17986365 | 2 |
| #22587635 | 2 |
| C2×#17985738 | 2 |
| C2×#330×C71 | 2 |
| C2×#1656 | 71 |