Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
672 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#17988527 | C2 | semidirect |
| 4. #22610022 | C2 | semidirect |
| 5. C2×#17988312 | C2 | semidirect |
| 6. #22607810 | C2 | semidirect |
| 247. C73 | #9921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988903 | 2 |
| #22615675 | 2 |
| C2×#17988527 | 2 |
| #22610022 | 2 |
| C2×#17988312 | 2 |
| #22607810 | 2 |
| C2×#327×C73 | 2 |
| #9921 | 73 |