Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
178 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 81 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. #17989695 | C4 | semidirect |
| 9. C2×#14556681 | C4 | semidirect |
| 79. C73 | #7470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989695 | 2 |
| C22×#14556681 | 2 |
| #22626140 | 2 |
| #7470 | 73 |