Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22586354 | C2 | semidirect |
| 4. C2×#341×C71 | C2 | semidirect |
| 15. C22⋊(C71⋊C16) | C22 | semidirect |
| 19. #341×C71 | C22 | semidirect |
| 156. C2×#341 | D71 | semidirect |
| 158. C71 | #11711 | semidirect |
| 173. #341 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986235 | 2 |
| #22589951 | 2 |
| #22586354 | 2 |
| C2×#341×C71 | 2 |
| #11711 | 71 |