Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 7. #17989515 | C4 | semidirect |
| 11. C2×#14556497 | C4 | semidirect |
| 14. C2×C32×C73 | C4 | semidirect |
| 77. C73 | #7473 | semidirect |
| 84. C2×C32 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#368 | 2 |
| #22626282 | 2 |
| C2×C32×D73 | 2 |
| #7473 | 73 |