Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 2. #22626097 | C2 | semidirect |
| 4. #22625447 | C2 | semidirect |
| 5. #22624827 | C2 | semidirect |
| 6. #22624800 | C2 | semidirect |
| 24. #17988883 | C4 | semidirect |
| 25. #17988879 | C4 | semidirect |
| 26. #17988877 | C4 | semidirect |
| 32. #476×C73 | C4 | semidirect |
| 221. C73 | #9321 | semidirect |
| 227. #476 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626854 | 2 |
| #22626097 | 2 |
| #22625805 | 2 |
| #22625447 | 2 |
| #22624827 | 2 |
| #22624800 | 2 |
| #22619743 | 2 |
| #9321 | 73 |