Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
490 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 490 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. #22626110 | C2 | semidirect |
| 4. #22625441 | C2 | semidirect |
| 5. #22624827 | C2 | semidirect |
| 6. #22624800 | C2 | semidirect |
| 25. #17988798 | C4 | semidirect |
| 27. #17988794 | C4 | semidirect |
| 28. #17988792 | C4 | semidirect |
| 32. #461×C73 | C4 | semidirect |
| 231. C73 | #9320 | semidirect |
| 240. #461 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626854 | 2 |
| #22626110 | 2 |
| #22625805 | 2 |
| #22625441 | 2 |
| #22624827 | 2 |
| #22624800 | 2 |
| #22619413 | 2 |
| #9320 | 73 |