Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
282 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 152 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. #22624848 | C2 | semidirect |
| 4. #22624847 | C2 | semidirect |
| 26. #14556531 | C8 | semidirect |
| 33. M32×C73 | C8 | semidirect |
| 83. C73 | #11406 | semidirect |
| 100. M32 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989476 | 2 |
| #22625134 | 2 |
| #22624848 | 2 |
| #22624847 | 2 |
| M32×Dic73 | 2 |
| #11406 | 73 |