Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
308 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22586514 | C2 | semidirect |
| 4. #22586499 | C2 | semidirect |
| 6. #17986611 | C4 | semidirect |
| 8. #17986378 | C4 | semidirect |
| 9. #17986367 | C4 | semidirect |
| 15. #17986060 | C4 | semidirect |
| 148. C71 | #13608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599423 | 2 |
| #22590029 | 2 |
| #22586514 | 2 |
| #22586499 | 2 |
| C71×#2129 | 2 |
| #13608 | 71 |