Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
266 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 19. #17988362 | C4 | semidirect |
| 20. C4×#11924003 | C4 | semidirect |
| 21. C16×Dic73 | C4 | semidirect |
| 22. #346×C73 | C4 | semidirect |
| 111. C73 | #12911 | semidirect |
| 124. #346 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#368 | 2 |
| #22626282 | 2 |
| #22626278 | 2 |
| #22625850 | 2 |
| #22611529 | 2 |
| #12911 | 73 |