Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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. C22×#14556666 | C2 | semidirect |
| 2. C2×#17989505 | C2 | semidirect |
| 3. #22625810 | C2 | semidirect |
| 4. #22625005 | C2 | semidirect |
| 28. #14556666 | D4 | semidirect |
| 162. C22×C73 | #361 | semidirect |
| 196. C73 | #13067 | semidirect |
| 364. C22 | #17989505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556666 | 2 |
| C2×#17989505 | 2 |
| #22625810 | 2 |
| #22625005 | 2 |
| #466×D73 | 2 |
| #13067 | 73 |