Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 27. #17988922 | C4 | semidirect |
| 30. #17988745 | C4 | semidirect |
| 32. #17988742 | C4 | semidirect |
| 34. #484×C73 | C4 | semidirect |
| 107. C22⋊#64408 | Q16 | semidirect |
| 258. C73 | #9276 | semidirect |
| 263. #484 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626463 | 2 |
| #22626121 | 2 |
| #22625369 | 2 |
| C2×#17989440 | 2 |
| #22624806 | 2 |
| #22624772 | 2 |
| #22620705 | 2 |
| #9276 | 73 |