Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
226 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22587237 | C2 | semidirect |
| 3. #22586414 | C2 | semidirect |
| 4. #22586304 | C2 | semidirect |
| 6. #22586259 | C2 | semidirect |
| 88. C71⋊C8 | SD32 | semidirect |
| 113. C71 | #12070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22587237 | 2 |
| D8×C71⋊C8 | 2 |
| #22586414 | 2 |
| #22586304 | 2 |
| #22586301 | 2 |
| #22586259 | 2 |
| C4×SD32×C71 | 2 |
| #12070 | 71 |