Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 1. #22627165 | C2 | semidirect |
| 2. #22627164 | C2 | semidirect |
| 3. C2×#17989696 | C2 | semidirect |
| 4. #22627162 | C2 | semidirect |
| 8. #17989696 | C22 | semidirect |
| 9. #17989695 | C22 | semidirect |
| 10. #17989694 | C22 | semidirect |
| 11. C2×#14556681 | C22 | semidirect |
| 91. C73 | #33974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627165 | 2 |
| #22627164 | 2 |
| C2×#17989696 | 2 |
| #22627162 | 2 |
| #22626896 | 2 |
| #33974 | 73 |