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. #22620667 | C2 | semidirect |
| 2. #22618836 | C2 | semidirect |
| 3. #22612144 | C2 | semidirect |
| 4. #22612103 | C2 | semidirect |
| 5. #22612102 | C2 | semidirect |
| 6. #22612004 | C2 | semidirect |
| 7. #22611875 | C2 | semidirect |
| 8. #22611832 | C2 | semidirect |
| 9. #22611830 | C2 | semidirect |
| 10. #22611742 | C2 | semidirect |
| 11. C73×#2213 | C2 | semidirect |
| 16. #17988985 | C22 | semidirect |
| 26. #17988699 | C22 | semidirect |
| 30. #17988411 | C22 | semidirect |
| 31. #17988410 | C22 | semidirect |
| 32. #17988408 | C22 | semidirect |
| 33. #17988400 | C22 | semidirect |
| 37. #17988364 | C22 | semidirect |
| 39. #493×C73 | C22 | semidirect |
| 41. #364×C73 | C22 | semidirect |
| 42. #361×C73 | C22 | semidirect |
| 109. Dic292 | #41 | semidirect |
| 114. D584 | #41 | semidirect |
| 142. Q16×C73 | #41 | semidirect |
| 148. D8×C73 | #41 | semidirect |
| 227. #2213 | D73 | semidirect |
| 232. C73 | #33688 | semidirect |
| 239. #493 | C2×D73 | semidirect |
| 257. #364 | C2×D73 | semidirect |
| 259. #361 | C2×D73 | semidirect |
| 336. Q16 | #11924027 | semidirect |
| 347. D8 | #11924027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620667 | 2 |
| #22618836 | 2 |
| #22612144 | 2 |
| #22612103 | 2 |
| #22612102 | 2 |
| #22612004 | 2 |
| #22611875 | 2 |
| #22611832 | 2 |
| #22611830 | 2 |
| #22611742 | 2 |
| C73×#2213 | 2 |
| #33688 | 73 |