Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 147 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×#17988370 | C2 | semidirect |
| 3. #22611542 | C2 | semidirect |
| 4. #22608019 | C2 | semidirect |
| 5. C23×C16×C73 | C2 | semidirect |
| 52. C2×C16×C73 | D4 | semidirect |
| 123. C22×C73 | #350 | semidirect |
| 140. C23×C16 | D73 | semidirect |
| 145. C73 | #12983 | semidirect |
| 187. C2×C16 | C22⋊D73 | semidirect |
| 265. C22 | #17988370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618625 | 2 |
| C2×#17988370 | 2 |
| #22611542 | 2 |
| #22608019 | 2 |
| C23×C16×C73 | 2 |
| #12983 | 73 |