Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 144 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. #22624845 | C2 | semidirect |
| 4. C16×#10596833 | C2 | semidirect |
| 39. C2×#10596833 | C16 | semidirect |
| 100. C73 | #11410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626289 | 2 |
| C2×C8×#10596833 | 2 |
| #22624845 | 2 |
| C16×#10596833 | 2 |
| #22611727 | 2 |
| #11410 | 73 |