Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22587103 | C2 | semidirect |
| 3. #22586302 | C2 | semidirect |
| 4. C71×#2162 | C2 | semidirect |
| 14. #17985752 | C22 | semidirect |
| 19. C4×C16×C71 | C22 | semidirect |
| 127. #2162 | D71 | semidirect |
| 130. C71 | #11661 | semidirect |
| 143. C4×C16 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D568 | 2 |
| #22587103 | 2 |
| #22586302 | 2 |
| C71×#2162 | 2 |
| #11661 | 71 |