Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 128 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×#17989479 | C2 | semidirect |
| 3. #22624976 | C2 | semidirect |
| 6. #17989484 | C4 | semidirect |
| 123. C73 | #12608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989484 | 2 |
| C2×#17989479 | 2 |
| #22624976 | 2 |
| C2×#17988541 | 2 |
| #12608 | 73 |