Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 100 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×#14556664 | C2 | semidirect |
| 2. C2×#17989502 | C2 | semidirect |
| 3. #22625811 | C2 | semidirect |
| 4. #22624992 | C2 | semidirect |
| 28. #14556664 | D4 | semidirect |
| 153. C22×C73 | #359 | semidirect |
| 163. C2×D73 | #359 | semidirect |
| 186. C73 | #13063 | semidirect |
| 344. C22 | #17989502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556664 | 2 |
| C2×#17989502 | 2 |
| #22625811 | 2 |
| #22624992 | 2 |
| #22619514 | 2 |
| #13063 | 73 |