Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1394 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1394 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 |
|---|---|---|
| 1. #22626378 | C2 | semidirect |
| 2. #22626071 | C2 | semidirect |
| 3. #22625762 | C2 | semidirect |
| 18. C2×#14556588 | C4 | semidirect |
| 19. C2×#14556580 | C4 | semidirect |
| 21. C2×#14556553 | C4 | semidirect |
| 23. C2×C4⋊Q8×C73 | C4 | semidirect |
| 182. C73 | #21794 | semidirect |
| 188. C2×C4⋊Q8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626378 | 2 |
| #22626071 | 2 |
| #22625762 | 2 |
| C2×#17989138 | 2 |
| #21794 | 73 |