Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 2. #22587114 | C2 | semidirect |
| 3. #22586990 | C2 | semidirect |
| 4. #22586899 | C2 | semidirect |
| 5. #22586661 | C2 | semidirect |
| 6. #22586198 | C2 | semidirect |
| 7. C71×#1804 | C2 | semidirect |
| 193. #1804 | D71 | semidirect |
| 199. C71 | #10464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597804 | 2 |
| #22587114 | 2 |
| #22586990 | 2 |
| #22586899 | 2 |
| #22586661 | 2 |
| #22586198 | 2 |
| C71×#1804 | 2 |
| #10464 | 71 |