Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 102 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. #22626146 | C2 | semidirect |
| 4. #22625740 | C2 | semidirect |
| 5. #22625003 | C2 | semidirect |
| 6. #22624997 | C2 | semidirect |
| 12. #17989628 | C4 | semidirect |
| 13. #17989628 | C4 | semidirect |
| 19. #17989499 | C4 | semidirect |
| 26. #17988401 | C4 | semidirect |
| 27. #17988400 | C4 | semidirect |
| 28. #17988399 | C4 | semidirect |
| 29. #361×C73 | C4 | semidirect |
| 42. #14556664 | C2×C4 | semidirect |
| 43. #14556660 | C2×C4 | semidirect |
| 64. #14556531 | C2×C4 | semidirect |
| 67. #14556527 | C2×C4 | semidirect |
| 70. M32×C73 | C2×C4 | semidirect |
| 71. #108×C73 | C2×C4 | semidirect |
| 187. C73 | #12647 | semidirect |
| 205. #361 | #64408 | semidirect |
| 234. M32 | C2×#64408 | semidirect |
| 239. #108 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989628 | 2 |
| #22626240 | 2 |
| #22626146 | 2 |
| #22625740 | 2 |
| #22625003 | 2 |
| #22624997 | 2 |
| #361×D73 | 2 |
| #12647 | 73 |