Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. #22625355 | C2 | semidirect |
| 4. #22625354 | C2 | semidirect |
| 5. #22624791 | C2 | semidirect |
| 6. #22624791 | C2 | semidirect |
| 21. #17988935 | C4 | semidirect |
| 22. #17988934 | C4 | semidirect |
| 23. #17988933 | C4 | semidirect |
| 26. #486×C73 | C4 | semidirect |
| 47. #14556591 | C2×C4 | semidirect |
| 63. C4×#10596831 | C2×C4 | semidirect |
| 64. C4⋊Q8×C73 | C2×C4 | semidirect |
| 67. C4×C8×C73 | C2×C4 | semidirect |
| 194. C73 | #9425 | semidirect |
| 201. #486 | #64408 | semidirect |
| 220. C4⋊Q8 | C2×#64408 | semidirect |
| 248. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626475 | 2 |
| #22625459 | 2 |
| #22625355 | 2 |
| #22625354 | 2 |
| #22624791 | 2 |
| #22620302 | 2 |
| #9425 | 73 |