Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. C2×#17985815 | C2 | semidirect |
| 4. #22589256 | C2 | semidirect |
| 5. #22586452 | C2 | semidirect |
| 6. #22586427 | C2 | semidirect |
| 24. #510×C71 | C4 | semidirect |
| 174. C71 | #13031 | semidirect |
| 179. #510 | Dic71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597257 | 2 |
| #22590089 | 2 |
| C2×#17985815 | 2 |
| #22589256 | 2 |
| #22586452 | 2 |
| #22586427 | 2 |
| C2×#510×C71 | 2 |
| #13031 | 71 |