Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
564 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. #22626463 | C2 | semidirect |
| 3. #22625369 | C2 | semidirect |
| 5. #22624806 | C2 | semidirect |
| 6. #22624772 | C2 | semidirect |
| 26. #17988918 | C4 | semidirect |
| 27. #17988915 | C4 | semidirect |
| 31. #17988738 | C4 | semidirect |
| 34. #450×C73 | C4 | semidirect |
| 109. C22⋊#64408 | SD16 | semidirect |
| 277. C73 | #9278 | semidirect |
| 286. #450 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626463 | 2 |
| #22626070 | 2 |
| #22625369 | 2 |
| C2×#17989438 | 2 |
| #22624806 | 2 |
| #22624772 | 2 |
| #22620685 | 2 |
| #9278 | 73 |