Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
444 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 100 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. #22625589 | C2 | semidirect |
| 4. #22625129 | C2 | semidirect |
| 5. #22624825 | C2 | semidirect |
| 6. #22624820 | C2 | semidirect |
| 8. #17989638 | C4 | semidirect |
| 9. Q8×#10596833 | C4 | semidirect |
| 10. #17989622 | C4 | semidirect |
| 13. D4×#10596833 | C4 | semidirect |
| 29. #17988328 | C4 | semidirect |
| 30. #17988328 | C4 | semidirect |
| 31. #17988327 | C4 | semidirect |
| 32. #329×C73 | C4 | semidirect |
| 187. C73 | #8247 | semidirect |
| 208. #329 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626745 | 2 |
| #22625589 | 2 |
| #22625303 | 2 |
| #22625129 | 2 |
| #22624825 | 2 |
| #22624820 | 2 |
| #22608516 | 2 |
| #8247 | 73 |