Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 6. #17989682 | C4 | semidirect |
| 7. #64408⋊C16 | C4 | semidirect |
| 108. C73 | #12593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64408⋊M32 | 2 |
| #22627004 | 2 |
| #22627003 | 2 |
| #22625587 | 2 |
| #12593 | 73 |