Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
556 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22598716 | C2 | semidirect |
| 3. #22589179 | C2 | semidirect |
| 4. #22586932 | C2 | semidirect |
| 5. #22586761 | C2 | semidirect |
| 6. #22586229 | C2 | semidirect |
| 7. C71×#3254 | C2 | semidirect |
| 193. #3254 | D71 | semidirect |
| 200. C71 | #10112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599255 | 2 |
| #22598716 | 2 |
| #22589179 | 2 |
| #22586932 | 2 |
| #22586761 | 2 |
| #22586229 | 2 |
| C71×#3254 | 2 |
| #10112 | 71 |