Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
322 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 3. #22625078 | C2 | semidirect |
| 12. C2×#14556583 | C4 | semidirect |
| 15. #17988942 | C4 | semidirect |
| 19. C4×M16×C73 | C4 | semidirect |
| 136. C73 | #13604 | semidirect |
| 147. C4×M16 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626224 | 2 |
| #22626204 | 2 |
| #22625078 | 2 |
| #22620332 | 2 |
| #13604 | 73 |