Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
426 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 23. #17988392 | C4 | semidirect |
| 24. #17988391 | C4 | semidirect |
| 25. #17988390 | C4 | semidirect |
| 26. #358×C73 | C4 | semidirect |
| 91. Dic292 | C4⋊C4 | semidirect |
| 104. Q16×C73 | C4⋊C4 | semidirect |
| 180. C73 | #12936 | semidirect |
| 198. #358 | #64408 | semidirect |
| 256. Q16 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#64408 | 2 |
| C2×#17989513 | 2 |
| C2×#17989500 | 2 |
| #22626035 | 2 |
| #22624988 | 2 |
| #22624968 | 2 |
| #358×D73 | 2 |
| #12936 | 73 |