Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
206 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 88 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. #22625092 | C2 | direct (N × H) |
| 8. C2×#14556497 | C4 | semidirect |
| 9. C32×D73 | C4 | semidirect |
| 11. C2×C32×C73 | C4 | semidirect |
| 21. #14556497 | C2×C4 | semidirect |
| 23. C32×C73 | C2×C4 | semidirect |
| 62. C2×C73 | #1423 | semidirect |
| 64. D73 | #1423 | semidirect |
| 70. C73 | C2×#1423 | semidirect |
| 76. C2×C32 | #64408 | semidirect |
| 90. C32 | C2×#64408 | semidirect |
| 131. C2 | #22625092 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989513 | 2 |
| #22625092 | 2 |
| C2×C32×D73 | 2 |
| C2×#1423 | 73 |