Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1050 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 184 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. #22626423 | C2 | semidirect |
| 2. #22626063 | C2 | semidirect |
| 3. #22625926 | C2 | semidirect |
| 4. #22625853 | C2 | semidirect |
| 5. #22625649 | C2 | semidirect |
| 18. #17988964 | C4 | semidirect |
| 19. #17988963 | C4 | semidirect |
| 20. #17988962 | C4 | semidirect |
| 22. #493×C73 | C4 | semidirect |
| 36. C2×D584 | C2×C4 | semidirect |
| 37. C2×#11924013 | C2×C4 | semidirect |
| 40. #14556588 | C2×C4 | semidirect |
| 42. #14556587 | C2×C4 | semidirect |
| 44. C4×#10596831 | C2×C4 | semidirect |
| 45. C8×Dic73 | C2×C4 | semidirect |
| 46. C2×D8×C73 | C2×C4 | semidirect |
| 47. #127×C73 | C2×C4 | semidirect |
| 48. C4×C8×C73 | C2×C4 | semidirect |
| 135. C73 | #22276 | semidirect |
| 142. #493 | #64408 | semidirect |
| 158. C2×D8 | C2×#64408 | semidirect |
| 164. #127 | C2×#64408 | semidirect |
| 175. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626423 | 2 |
| #22626063 | 2 |
| #22625926 | 2 |
| #22625853 | 2 |
| #22625649 | 2 |
| #493×D73 | 2 |
| #22276 | 73 |