Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22597224 | C2 | semidirect |
| 3. C2×#17985810 | C2 | semidirect |
| 4. #22589236 | C2 | semidirect |
| 5. #22586445 | C2 | semidirect |
| 6. #22586425 | C2 | semidirect |
| 7. C71×#2145 | C2 | semidirect |
| 11. #17986439 | C4 | semidirect |
| 13. #17986434 | C4 | semidirect |
| 34. C2×Dic284 | C2×C4 | semidirect |
| 36. C2×D568 | C2×C4 | semidirect |
| 50. #14556068 | C2×C4 | semidirect |
| 192. #2145 | D71 | semidirect |
| 197. C71 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22597224 | 2 |
| C2×#17985810 | 2 |
| #22589236 | 2 |
| #22586445 | 2 |
| #22586425 | 2 |
| C71×#2145 | 2 |
| #13030 | 71 |