Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22627018 | C2 | semidirect |
| 4. #64408⋊C32 | C2 | semidirect |
| 6. #17989696 | C4 | semidirect |
| 7. #17989695 | C4 | semidirect |
| 8. #17989694 | C4 | semidirect |
| 12. C2×#14556681 | C4 | semidirect |
| 87. C73 | #13549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627162 | 2 |
| C2×#17989694 | 2 |
| #22627018 | 2 |
| #64408⋊C32 | 2 |
| #22626143 | 2 |
| #13549 | 73 |