Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
622 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 139 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. (C2×#10596842)⋊C4 | C4 | semidirect |
| 22. C2×C4⋊#64408 | C8 | semidirect |
| 32. C2×C4⋊Dic73 | C8 | semidirect |
| 36. C2×C4⋊C4×C73 | C8 | semidirect |
| 188. C73 | #7025 | semidirect |
| 215. C2×C4⋊C4 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C2×#10596842)⋊C4 | 2 |
| #22625108 | 2 |
| #7025 | 73 |