Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 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. #22590140 | C2 | semidirect |
| 3. #22590136 | C2 | semidirect |
| 4. #22586266 | C2 | semidirect |
| 5. #22586265 | C2 | semidirect |
| 6. #22586265 | C2 | semidirect |
| 7. C71×#1315 | C2 | semidirect |
| 172. #1315 | D71 | semidirect |
| 173. C71 | #11492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597048 | 2 |
| #22590140 | 2 |
| #22590136 | 2 |
| #22586266 | 2 |
| #22586265 | 2 |
| C71×#1315 | 2 |
| #11492 | 71 |