Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
684 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C4×#11924038 | C2 | semidirect |
| 2. #22625658 | C2 | semidirect |
| 3. C2×#17989442 | C2 | semidirect |
| 4. #22624807 | C2 | semidirect |
| 34. #14556646 | D4 | semidirect |
| 216. C73 | #9120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11924038 | 2 |
| #22625658 | 2 |
| C2×#17989442 | 2 |
| #22624807 | 2 |
| #22618231 | 2 |
| #9120 | 73 |