Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
222 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. #22625041 | C2 | semidirect |
| 4. #22625040 | C2 | semidirect |
| 9. #17989519 | C4 | semidirect |
| 10. #17989518 | C4 | semidirect |
| 16. #17988421 | C4 | semidirect |
| 18. C32×D73 | C4 | semidirect |
| 19. M64×C73 | C4 | semidirect |
| 30. #14556641 | C2×C4 | semidirect |
| 37. #14556497 | C2×C4 | semidirect |
| 39. C32×C73 | C2×C4 | semidirect |
| 91. D73 | #1398 | semidirect |
| 97. C73 | C2×#1398 | semidirect |
| 105. M64 | #64408 | semidirect |
| 131. C32 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626352 | 2 |
| C2×#17989474 | 2 |
| #22625041 | 2 |
| #22625040 | 2 |
| M64×D73 | 2 |
| C2×#1398 | 73 |