Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22590100 | C2 | semidirect |
| 4. #22588465 | C2 | semidirect |
| 5. #22586455 | C2 | semidirect |
| 6. #22586433 | C2 | semidirect |
| 10. #17986121 | C4 | semidirect |
| 150. C71 | #12829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597257 | 2 |
| #22590100 | 2 |
| #22590047 | 2 |
| #22588465 | 2 |
| #22586455 | 2 |
| #22586433 | 2 |
| C71×#2148 | 2 |
| #12829 | 71 |