Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 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 |
|---|---|---|
| 2. C2×#17985819 | C2 | semidirect |
| 3. C2×#17985813 | C2 | semidirect |
| 4. C2×#17985812 | C2 | semidirect |
| 5. #22590055 | C2 | semidirect |
| 6. #22588221 | C2 | semidirect |
| 7. C71×#2140 | C2 | semidirect |
| 13. #17986374 | C4 | semidirect |
| 47. #14556064 | D4 | semidirect |
| 64. #107×C71 | D4 | semidirect |
| 178. #2140 | D71 | semidirect |
| 180. C71 | #13261 | semidirect |
| 233. #107 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986374 | 2 |
| C2×#17985819 | 2 |
| C2×#17985813 | 2 |
| C2×#17985812 | 2 |
| #22590055 | 2 |
| #22588221 | 2 |
| C71×#2140 | 2 |
| #13261 | 71 |