Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
606 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 1. #22626053 | C2 | semidirect |
| 2. C2×#17989450 | C2 | semidirect |
| 3. C2×#17989435 | C2 | semidirect |
| 4. C2×C8×#10596833 | C2 | semidirect |
| 34. C2×D584 | C8 | semidirect |
| 54. C2×#10596833 | D8 | semidirect |
| 116. C8×C73 | C22⋊C8 | semidirect |
| 150. C73 | #9657 | semidirect |
| 262. C8 | #14556648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626053 | 2 |
| C2×#17989450 | 2 |
| C2×#17989435 | 2 |
| C2×C8×#10596833 | 2 |
| C2×#17988669 | 2 |
| #9657 | 73 |