Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
466 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 136 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. #22624972 | C2 | semidirect |
| 6. C22⋊#11924031 | C4 | semidirect |
| 123. C73 | #12606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626158 | 2 |
| C2×#17989479 | 2 |
| #22624972 | 2 |
| C2×#17988543 | 2 |
| #12606 | 73 |