Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
862 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 862 conjugacy classes of subgroups — too many to draw. Only its 469 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. C2×C4⋊#11924040 | C2 | direct (N × H) |
| 6. C4⋊#11924040 | C22 | direct (N × H) |
| 44. C22×C4×C73 | C16 | semidirect |
| 50. C2×C4×C73 | C2×C16 | semidirect |
| 63. C22×C73 | C4⋊C16 | semidirect |
| 68. C4×C73 | C22×C16 | semidirect |
| 74. C2×C73 | C2×C4⋊C16 | semidirect |
| 81. C73 | C22×C4⋊C16 | semidirect |
| 112. C22×C4 | #11924040 | semidirect |
| 135. C2×C4 | C2×#11924040 | semidirect |
| 141. C22 | C4⋊#11924040 | direct (N × H) |
| 150. C4 | C22×#11924040 | semidirect |
| 151. C2 | C2×C4⋊#11924040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924040 | 2 |
| C2×C4⋊#11924040 | 2 |
| C22×C4×#10596833 | 2 |
| C22×C4⋊C16 | 73 |