Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
464 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22588523 | C2 | semidirect |
| 5. #22586225 | C2 | semidirect |
| 6. #22586186 | C2 | semidirect |
| 7. C71×#1855 | C2 | semidirect |
| 22. #17985737 | C4 | semidirect |
| 23. #17985737 | C4 | semidirect |
| 24. #17985734 | C4 | semidirect |
| 25. #17985734 | C4 | semidirect |
| 220. #1855 | D71 | semidirect |
| 225. C71 | #8874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597390 | 2 |
| #22588642 | 2 |
| #22588523 | 2 |
| #22586832 | 2 |
| #22586225 | 2 |
| #22586186 | 2 |
| C71×#1855 | 2 |
| #8874 | 71 |