Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22620670 | C2 | semidirect |
| 2. #22618836 | C2 | semidirect |
| 3. #22612147 | C2 | semidirect |
| 4. #22612099 | C2 | semidirect |
| 5. #22612008 | C2 | semidirect |
| 6. #22612007 | C2 | semidirect |
| 7. #22611878 | C2 | semidirect |
| 8. #22611828 | C2 | semidirect |
| 9. #22611826 | C2 | semidirect |
| 10. #22611742 | C2 | semidirect |
| 11. C73×#2230 | C2 | semidirect |
| 17. #17988964 | C22 | semidirect |
| 27. #17988698 | C22 | semidirect |
| 31. #17988409 | C22 | semidirect |
| 32. #17988408 | C22 | semidirect |
| 33. #17988401 | C22 | semidirect |
| 34. #17988399 | C22 | semidirect |
| 37. #17988364 | C22 | semidirect |
| 38. #498×C73 | C22 | semidirect |
| 40. #365×C73 | C22 | semidirect |
| 41. #364×C73 | C22 | semidirect |
| 111. Dic292 | #41 | semidirect |
| 120. D584 | #41 | semidirect |
| 144. Q16×C73 | #41 | semidirect |
| 146. D8×C73 | #41 | semidirect |
| 225. #2230 | D73 | semidirect |
| 232. C73 | #33688 | semidirect |
| 238. #498 | C2×D73 | semidirect |
| 255. #365 | C2×D73 | semidirect |
| 257. #364 | C2×D73 | semidirect |
| 336. Q16 | #11924029 | semidirect |
| 347. D8 | #11924029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620670 | 2 |
| #22618836 | 2 |
| #22612147 | 2 |
| #22612099 | 2 |
| #22612008 | 2 |
| #22612007 | 2 |
| #22611878 | 2 |
| #22611828 | 2 |
| #22611826 | 2 |
| #22611742 | 2 |
| C73×#2230 | 2 |
| #33688 | 73 |