Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
394 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 112 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×#17989476 | C2 | semidirect |
| 2. #22625478 | C2 | semidirect |
| 3. #22624892 | C2 | semidirect |
| 4. #22624890 | C2 | semidirect |
| 30. #14556613 | C8 | semidirect |
| 153. C73 | #11597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989476 | 2 |
| #22625478 | 2 |
| #22624892 | 2 |
| #22624890 | 2 |
| #22618702 | 2 |
| #11597 | 73 |