Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 27. #17988329 | C4 | semidirect |
| 28. #17988328 | C4 | semidirect |
| 29. #17988328 | C4 | semidirect |
| 30. #330×C73 | C4 | semidirect |
| 167. C73 | #8919 | semidirect |
| 190. #330 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626844 | 2 |
| #22626118 | 2 |
| #22625497 | 2 |
| #22625496 | 2 |
| #22624820 | 2 |
| #22608524 | 2 |
| #8919 | 73 |