Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22588352 | C2 | semidirect |
| 3. #22587112 | C2 | semidirect |
| 6. #22586663 | C2 | semidirect |
| 7. C71×#1286 | C2 | semidirect |
| 188. #1286 | D71 | semidirect |
| 189. C71 | #10467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597814 | 2 |
| #22588352 | 2 |
| #22587112 | 2 |
| #22586987 | 2 |
| #22586899 | 2 |
| #22586663 | 2 |
| C71×#1286 | 2 |
| #10467 | 71 |