Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 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. #349×D71 | C2 | semidirect |
| 3. #22586278 | C2 | semidirect |
| 4. #22586277 | C2 | semidirect |
| 5. C71×#1321 | C2 | semidirect |
| 15. #17985781 | C22 | semidirect |
| 18. #349×C71 | C22 | semidirect |
| 181. #1321 | D71 | semidirect |
| 182. C71 | #11438 | semidirect |
| 195. #349 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596782 | 2 |
| #349×D71 | 2 |
| #22586278 | 2 |
| #22586277 | 2 |
| C71×#1321 | 2 |
| #11438 | 71 |