Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
200 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 54 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. Q32×#64408 | C2 | semidirect |
| 3. #22625092 | C2 | semidirect |
| 4. #22625081 | C2 | semidirect |
| 6. #22625037 | C2 | semidirect |
| 18. #17988426 | C4 | semidirect |
| 19. #17988425 | C4 | semidirect |
| 20. #17988424 | C4 | semidirect |
| 22. SD64×C73 | C4 | semidirect |
| 34. Dic584 | C2×C4 | semidirect |
| 39. #14556497 | C2×C4 | semidirect |
| 40. Q32×C73 | C2×C4 | semidirect |
| 42. C32×C73 | C2×C4 | semidirect |
| 106. C73 | #13652 | semidirect |
| 114. SD64 | #64408 | semidirect |
| 128. Q32 | C2×#64408 | semidirect |
| 141. C32 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×#64408 | 2 |
| D16×#64408 | 2 |
| #22625092 | 2 |
| #22625081 | 2 |
| #22625080 | 2 |
| #22625037 | 2 |
| SD64×D73 | 2 |
| #13652 | 73 |