Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 112 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×#17989482 | C2 | semidirect |
| 2. C2×#17989461 | C2 | semidirect |
| 3. #22624917 | C2 | direct (N × H) |
| 8. #17989482 | C22 | semidirect |
| 10. #17989461 | C22 | semidirect |
| 15. #17988820 | C4 | semidirect |
| 17. C2×#14556525 | C4 | semidirect |
| 19. C22×D8×C73 | C4 | semidirect |
| 42. #14556525 | C2×C4 | semidirect |
| 48. C2×D8×C73 | C2×C4 | semidirect |
| 159. C2×C73 | #1347 | semidirect |
| 170. C73 | C2×#1347 | semidirect |
| 171. C22×D8 | #64408 | semidirect |
| 192. C2×D8 | C2×#64408 | semidirect |
| 327. C2 | #22624917 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989482 | 2 |
| C2×#17989461 | 2 |
| #22624917 | 2 |
| C2×#17988820 | 2 |
| C2×#1347 | 73 |