Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22589951 | C2 | semidirect |
| 3. #22586263 | C2 | semidirect |
| 4. C2×C22⋊C16×C71 | C2 | semidirect |
| 166. C2×C22⋊C16 | D71 | semidirect |
| 168. C71 | #11419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985965 | 2 |
| #22589951 | 2 |
| #22586263 | 2 |
| C2×C22⋊C16×C71 | 2 |
| #11419 | 71 |