Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
376 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 5. #17989465 | C4 | semidirect |
| 7. C2×C4⋊#10596831 | C4 | semidirect |
| 9. C2×C4×C8×C73 | C4 | semidirect |
| 115. C73 | #7237 | semidirect |
| 120. C2×C4×C8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625792 | 2 |
| #22610725 | 2 |
| #7237 | 73 |