Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 124 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×#17989477 | C2 | semidirect |
| 4. #22624971 | C2 | semidirect |
| 14. #17989482 | C4 | semidirect |
| 15. C22⋊#11924031 | C4 | semidirect |
| 19. C22⋊#11924003 | C4 | semidirect |
| 20. #17988366 | C4 | semidirect |
| 21. C22⋊C16×C73 | C4 | semidirect |
| 36. C2×#11924031 | C2×C4 | semidirect |
| 51. C2×#11924003 | C2×C4 | semidirect |
| 53. C2×C16×C73 | C2×C4 | semidirect |
| 138. C22×C73 | #347 | semidirect |
| 146. C2×D73 | #347 | semidirect |
| 170. C73 | #12605 | semidirect |
| 185. C22⋊C16 | #64408 | semidirect |
| 214. C2×C16 | C2×#64408 | semidirect |
| 312. C22 | #17989477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556645 | 2 |
| #22626159 | 2 |
| C2×#17989477 | 2 |
| #22624971 | 2 |
| #22611540 | 2 |
| #12605 | 73 |