Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
728 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 120 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×#17989605 | C2 | semidirect |
| 2. #22625788 | C2 | semidirect |
| 3. C2×#17989445 | C2 | semidirect |
| 4. #22624809 | C2 | semidirect |
| 30. #14556658 | D4 | semidirect |
| 248. C73 | #9134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989605 | 2 |
| #22625788 | 2 |
| C2×#17989445 | 2 |
| #22624809 | 2 |
| #22618275 | 2 |
| #9134 | 73 |