Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
462 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#17985797 | C2 | semidirect |
| 4. #22588731 | C2 | semidirect |
| 5. #22588557 | C2 | semidirect |
| 6. #22586466 | C2 | semidirect |
| 226. C71 | #13427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22595348 | 2 |
| C2×#17985797 | 2 |
| #22588744 | 2 |
| #22588731 | 2 |
| #22588557 | 2 |
| #22586466 | 2 |
| C2×#355×C71 | 2 |
| #13427 | 71 |