Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
340 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22590142 | C2 | semidirect |
| 3. #22587087 | C2 | semidirect |
| 4. #22586395 | C2 | semidirect |
| 5. #22586387 | C2 | semidirect |
| 6. #22586385 | C2 | semidirect |
| 7. C71×#1364 | C2 | semidirect |
| 141. #1364 | D71 | semidirect |
| 144. C71 | #11951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598920 | 2 |
| #22590142 | 2 |
| #22587087 | 2 |
| #22586395 | 2 |
| #22586387 | 2 |
| #22586385 | 2 |
| C71×#1364 | 2 |
| #11951 | 71 |