Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
556 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#14556069 | C2 | semidirect |
| 2. C2×#17986269 | C2 | semidirect |
| 3. C2×#17985812 | C2 | semidirect |
| 4. C2×#17985811 | C2 | semidirect |
| 5. #22589954 | C2 | semidirect |
| 6. #22586433 | C2 | semidirect |
| 7. C2×#472×C71 | C2 | semidirect |
| 200. C2×#472 | D71 | semidirect |
| 205. C71 | #13313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556069 | 2 |
| C2×#17986269 | 2 |
| C2×#17985812 | 2 |
| C2×#17985811 | 2 |
| #22589954 | 2 |
| #22586433 | 2 |
| C2×#472×C71 | 2 |
| #13313 | 71 |