Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×C4⋊#11924040 | C2 | semidirect |
| 2. C2×C4×#11924040 | C2 | semidirect |
| 3. D4⋊#11924040 | C2 | direct (N × H) |
| 8. C4⋊#11924040 | C22 | semidirect |
| 10. C4×#11924040 | C22 | semidirect |
| 80. C2×D4×C73 | C16 | semidirect |
| 90. D4×C73 | C2×C16 | semidirect |
| 132. C2×C73 | D4⋊C16 | semidirect |
| 140. C73 | C2×D4⋊C16 | semidirect |
| 187. C2×D4 | #11924040 | semidirect |
| 226. D4 | C2×#11924040 | semidirect |
| 267. C2 | D4⋊#11924040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11924040 | 2 |
| C2×C4×#11924040 | 2 |
| D4⋊#11924040 | 2 |
| C2×D4×#10596833 | 2 |
| C2×D4⋊C16 | 73 |