Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 122 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. #22624956 | C2 | semidirect |
| 4. #22624955 | C2 | semidirect |
| 34. M32×C73 | C8 | semidirect |
| 55. C16×C73 | C2×C8 | semidirect |
| 96. C73 | #12000 | semidirect |
| 114. M32 | #10596833 | semidirect |
| 146. C16 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625478 | 2 |
| C2×#17989448 | 2 |
| #22624956 | 2 |
| #22624955 | 2 |
| M32×Dic73 | 2 |
| #12000 | 73 |