Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1470 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 744 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 |
|---|---|---|
| 2. #22625863 | C2 | direct (N × H) |
| 24. C2×C42×C73 | C8 | semidirect |
| 44. C42×C73 | C2×C8 | semidirect |
| 49. C2×C4×C73 | C4⋊C8 | semidirect |
| 68. C4×C73 | C2×C4⋊C8 | semidirect |
| 74. C2×C73 | #1842 | semidirect |
| 81. C73 | C2×#1842 | semidirect |
| 101. C2×C42 | #10596833 | semidirect |
| 122. C42 | C2×#10596833 | semidirect |
| 135. C2×C4 | C4⋊#10596833 | semidirect |
| 150. C4 | C2×C4⋊#10596833 | semidirect |
| 151. C2 | #22625863 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10596833 | 2 |
| #22625863 | 2 |
| C2×C42×Dic73 | 2 |
| C2×#1842 | 73 |