Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 20. #14556687 | C2×C4 | semidirect |
| 143. #64408 | #349 | semidirect |
| 161. C73 | C4×#349 | 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×M16×#64408 | 2 |
| C4×#349 | 73 |