Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
574 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22590704 | C2 | semidirect |
| 4. #22586788 | C2 | semidirect |
| 5. #22586234 | C2 | semidirect |
| 6. #22586196 | C2 | semidirect |
| 11. #17986291 | C4 | semidirect |
| 12. #17986196 | C4 | semidirect |
| 153. Dic142 | #104 | semidirect |
| 191. C71 | #9326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598458 | 2 |
| #22590704 | 2 |
| #22586848 | 2 |
| #22586788 | 2 |
| #22586234 | 2 |
| #22586196 | 2 |
| C71×#1980 | 2 |
| #9326 | 71 |