Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
614 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 138 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. C8×C22⋊#64408 | C2 | semidirect |
| 4. #22624773 | C2 | semidirect |
| 12. #17989432 | C4 | semidirect |
| 13. #17989431 | C4 | semidirect |
| 14. C22×C8×D73 | C4 | semidirect |
| 19. C2×#14556503 | C4 | semidirect |
| 21. C2×C4×#10596831 | C4 | semidirect |
| 22. C2×C4⋊C8×C73 | C4 | semidirect |
| 26. #14556650 | C8 | semidirect |
| 60. C22⋊#64408 | C2×C8 | semidirect |
| 106. C22×D73 | C4×C8 | semidirect |
| 119. C2×C4×C73 | C4×C8 | semidirect |
| 138. #10596831 | #99 | semidirect |
| 175. C73 | C8×#99 | semidirect |
| 181. C2×C4⋊C8 | #64408 | semidirect |
| 300. C2×C4 | C8×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556650 | 2 |
| C8×C22⋊#64408 | 2 |
| #22625168 | 2 |
| #22624773 | 2 |
| C2×#17988652 | 2 |
| C8×#99 | 73 |