Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
444 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22597325 | C2 | semidirect |
| 3. #22586969 | C2 | semidirect |
| 4. #22586784 | C2 | semidirect |
| 5. #22586680 | C2 | semidirect |
| 6. C71⋊#1308 | C2 | semidirect |
| 7. C71×#1291 | C2 | semidirect |
| 211. #1291 | D71 | semidirect |
| 212. C71 | #9532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598480 | 2 |
| #22597325 | 2 |
| #22586969 | 2 |
| #22586784 | 2 |
| #22586680 | 2 |
| C71⋊#1308 | 2 |
| C71×#1291 | 2 |
| #9532 | 71 |