Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
818 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 2. #22625029 | C2 | direct (N × H) |
| 7. C2×#14556652 | C4 | semidirect |
| 23. #14556652 | C2×C4 | semidirect |
| 167. C2×C73 | #1394 | semidirect |
| 174. C73 | C2×#1394 | semidirect |
| 337. C2 | #22625029 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556652 | 2 |
| #22625029 | 2 |
| C2×#17988492 | 2 |
| C2×#1394 | 73 |