Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
490 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 137 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. #64408⋊M32 | C2 | semidirect |
| 3. #22627008 | C2 | semidirect |
| 6. #17989686 | C4 | semidirect |
| 7. #17989685 | C4 | semidirect |
| 162. C73 | #12602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627105 | 2 |
| #64408⋊M32 | 2 |
| #22627008 | 2 |
| C2×#17989550 | 2 |
| #12602 | 73 |