Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
990 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 170 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. #22626369 | C2 | semidirect |
| 3. #22625634 | C2 | semidirect |
| 4. C2×#17989454 | C2 | semidirect |
| 9. #17989586 | C4 | semidirect |
| 18. #17988494 | C4 | semidirect |
| 19. #17988489 | C4 | semidirect |
| 20. #17988488 | C4 | semidirect |
| 23. #391×C73 | C4 | semidirect |
| 82. C4×#64408 | C22⋊C4 | semidirect |
| 100. C2×D292 | C42 | semidirect |
| 128. C2×Q8×C73 | C42 | semidirect |
| 232. C73 | #10949 | semidirect |
| 242. #391 | #64408 | semidirect |
| 308. C2×Q8 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989586 | 2 |
| #22626369 | 2 |
| #22625634 | 2 |
| C2×#17989454 | 2 |
| #22612522 | 2 |
| #10949 | 73 |