Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
294 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 14. #17985721 | C4 | semidirect |
| 15. #17985721 | C4 | semidirect |
| 16. #17985720 | C4 | semidirect |
| 17. C8×C71⋊C8 | C4 | semidirect |
| 116. C71 | #8141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22588092 | 2 |
| #22586633 | 2 |
| #22586624 | 2 |
| #22586170 | 2 |
| #22586169 | 2 |
| C71×#1274 | 2 |
| #8141 | 71 |