Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
696 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 114 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×#14556646 | C2 | semidirect |
| 2. #22625657 | C2 | semidirect |
| 3. C2×#17989442 | C2 | semidirect |
| 4. #22624807 | C2 | semidirect |
| 35. #14556646 | D4 | semidirect |
| 183. C22×C73 | #329 | semidirect |
| 216. C73 | #9119 | semidirect |
| 394. C22 | #17989442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556646 | 2 |
| #22625657 | 2 |
| C2×#17989442 | 2 |
| #22624807 | 2 |
| #22618230 | 2 |
| #9119 | 73 |