Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22586539 | C2 | semidirect |
| 3. #22586517 | C2 | semidirect |
| 4. C22⋊(C71⋊C32) | C2 | semidirect |
| 5. C2×#366×C71 | C2 | semidirect |
| 78. C2×#366 | D71 | semidirect |
| 82. C71 | #13711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590426 | 2 |
| #22586539 | 2 |
| #22586517 | 2 |
| C22⋊(C71⋊C32) | 2 |
| C2×#366×C71 | 2 |
| #13711 | 71 |