Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
582 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 122 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. #22625667 | C2 | semidirect |
| 4. #22624773 | C2 | semidirect |
| 12. #17989433 | C4 | semidirect |
| 13. #17989430 | C4 | semidirect |
| 14. C23×#10596831 | C4 | semidirect |
| 19. C2×#14556520 | C4 | semidirect |
| 21. C2×C8×Dic73 | C4 | semidirect |
| 22. C2×C22⋊C8×C73 | C4 | semidirect |
| 103. C23×C73 | #97 | semidirect |
| 128. C2×Dic73 | #97 | semidirect |
| 138. #10596831 | #99 | semidirect |
| 175. C73 | #8160 | semidirect |
| 185. C2×C22⋊C8 | #64408 | semidirect |
| 278. C23 | #14556645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556649 | 2 |
| #22625667 | 2 |
| #22625166 | 2 |
| #22624773 | 2 |
| C2×#17988650 | 2 |
| #8160 | 73 |