Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
410 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 3. #22586291 | C2 | semidirect |
| 4. #22586290 | C2 | semidirect |
| 5. C71×#1327 | C2 | semidirect |
| 158. D71 | #1327 | direct (N × H) |
| 163. #1327 | D71 | direct (N × H) |
| 164. C71 | C2×#1327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #423×D71 | 2 |
| #349×D71 | 2 |
| #22586291 | 2 |
| #22586290 | 2 |
| C71×#1327 | 2 |
| C2×#1327 | 71 |