Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1230 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 224 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. #22626213 | C2 | direct (N × H) |
| 3. C2×#17989493 | C2 | semidirect |
| 10. #17989493 | C22 | semidirect |
| 13. #17989161 | C4 | semidirect |
| 15. C2×#14556589 | C4 | semidirect |
| 19. C2×#14556550 | C4 | semidirect |
| 20. C23×Q8×C73 | C4 | semidirect |
| 39. #14556589 | C2×C4 | semidirect |
| 48. #14556550 | C2×C4 | semidirect |
| 59. C22×Q8×C73 | C2×C4 | semidirect |
| 188. C2×C73 | #2129 | semidirect |
| 196. C73 | C2×#2129 | semidirect |
| 198. C23×Q8 | #64408 | semidirect |
| 224. C22×Q8 | C2×#64408 | semidirect |
| 381. C2 | #22626213 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989566 | 2 |
| #22626213 | 2 |
| C2×#17989493 | 2 |
| C2×#17989161 | 2 |
| C2×#2129 | 73 |