Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22597357 | C2 | semidirect |
| 3. #22586939 | C2 | semidirect |
| 4. #22586772 | C2 | semidirect |
| 5. #22586693 | C2 | semidirect |
| 6. #22586229 | C2 | semidirect |
| 7. C71×#1307 | C2 | semidirect |
| 213. #1307 | D71 | semidirect |
| 215. C71 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597835 | 2 |
| #22597357 | 2 |
| #22586939 | 2 |
| #22586772 | 2 |
| #22586693 | 2 |
| #22586229 | 2 |
| C71×#1307 | 2 |
| #9350 | 71 |