Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 3. #22624946 | C2 | direct (N × H) |
| 131. C2×C73 | #1362 | semidirect |
| 139. C73 | C2×#1362 | semidirect |
| 265. C2 | #22624946 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989508 | 2 |
| C2×#17989451 | 2 |
| #22624946 | 2 |
| C2×#17988965 | 2 |
| C2×#1362 | 73 |