Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 1. #22625587 | C2 | semidirect |
| 4. C8×#11924038 | C2 | semidirect |
| 5. #22624824 | C2 | semidirect |
| 6. #22624818 | C2 | semidirect |
| 14. #17989444 | C4 | semidirect |
| 15. #17989442 | C4 | semidirect |
| 21. #17988714 | C4 | semidirect |
| 22. C8×Dic146 | C4 | semidirect |
| 23. #17988665 | C4 | semidirect |
| 30. C8×D4×C73 | C4 | semidirect |
| 179. C73 | #8247 | semidirect |
| 186. C8×D4 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625587 | 2 |
| #22625381 | 2 |
| #22625302 | 2 |
| C8×#11924038 | 2 |
| #22624824 | 2 |
| #22624818 | 2 |
| #22618903 | 2 |
| #8247 | 73 |