Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 136 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×#17989476 | C2 | semidirect |
| 2. C2×#17989448 | C2 | semidirect |
| 3. #22624889 | C2 | direct (N × H) |
| 8. #17989476 | C22 | semidirect |
| 10. #17989448 | C22 | semidirect |
| 45. C2×D8×C73 | C8 | semidirect |
| 76. D8×C73 | C2×C8 | semidirect |
| 127. C2×C73 | #1333 | semidirect |
| 135. C73 | C2×#1333 | semidirect |
| 155. C2×D8 | #10596833 | semidirect |
| 193. D8 | C2×#10596833 | semidirect |
| 257. C2 | #22624889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989476 | 2 |
| C2×#17989448 | 2 |
| #22624889 | 2 |
| C2×D8×Dic73 | 2 |
| C2×#1333 | 73 |