Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#17988352 | C2 | semidirect |
| 3. #22607950 | C2 | semidirect |
| 4. #22607947 | C2 | semidirect |
| 5. C2×C22⋊C16×C73 | C2 | semidirect |
| 172. C2×C22⋊C16 | D73 | semidirect |
| 176. C73 | #11709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619512 | 2 |
| C2×#17988352 | 2 |
| #22607950 | 2 |
| #22607947 | 2 |
| C2×C22⋊C16×C73 | 2 |
| #11709 | 73 |