Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
340 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. #22625077 | C2 | direct (N × H) |
| 14. #17988944 | C4 | semidirect |
| 18. C2×C4×#10596831 | C4 | semidirect |
| 19. C2×#125×C73 | C4 | semidirect |
| 40. C4×#10596831 | C2×C4 | semidirect |
| 43. #125×C73 | C2×C4 | semidirect |
| 132. C2×C73 | #1414 | semidirect |
| 140. C73 | C2×#1414 | semidirect |
| 141. C2×#125 | #64408 | semidirect |
| 162. #125 | C2×#64408 | semidirect |
| 269. C2 | #22625077 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989496 | 2 |
| C2×#17989494 | 2 |
| #22625077 | 2 |
| C2×#17988944 | 2 |
| C2×#1414 | 73 |