Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
754 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22589185 | C2 | semidirect |
| 3. #22587073 | C2 | semidirect |
| 4. #22586931 | C2 | semidirect |
| 5. #22586780 | C2 | semidirect |
| 6. #22586777 | C2 | semidirect |
| 7. C71×#1997 | C2 | semidirect |
| 236. #1997 | D71 | semidirect |
| 242. C71 | #8470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602253 | 2 |
| #22589185 | 2 |
| #22587073 | 2 |
| #22586931 | 2 |
| #22586780 | 2 |
| #22586777 | 2 |
| C71×#1997 | 2 |
| #8470 | 71 |