Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
834 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 147 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×#17988313 | C2 | semidirect |
| 2. #22607863 | C2 | direct (N × H) |
| 6. #17988313 | C22 | semidirect |
| 23. C22×D4×C73 | C8 | semidirect |
| 59. C2×D4×C73 | C2×C8 | semidirect |
| 159. C2×C73 | #1318 | semidirect |
| 166. C73 | C2×#1318 | semidirect |
| 183. C22×D4 | #10596831 | semidirect |
| 220. C2×D4 | C2×#10596831 | semidirect |
| 321. C2 | #22607863 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988313 | 2 |
| #22607863 | 2 |
| C2×#390×C73 | 2 |
| C2×#1318 | 73 |