Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 558 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. #22626855 | C2 | semidirect |
| 2. #22626098 | C2 | semidirect |
| 3. #22625806 | C2 | semidirect |
| 4. #22625439 | C2 | semidirect |
| 5. #22624827 | C2 | semidirect |
| 6. #22624800 | C2 | semidirect |
| 25. #17988787 | C4 | semidirect |
| 27. #17988783 | C4 | semidirect |
| 29. #17988779 | C4 | semidirect |
| 32. #460×C73 | C4 | semidirect |
| 252. C73 | #9322 | semidirect |
| 258. #460 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626855 | 2 |
| #22626098 | 2 |
| #22625806 | 2 |
| #22625439 | 2 |
| #22624827 | 2 |
| #22624800 | 2 |
| #22619408 | 2 |
| #9322 | 73 |