Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
408 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#17989511 | C2 | semidirect |
| 4. #22626036 | C2 | semidirect |
| 5. #22625005 | C2 | semidirect |
| 6. #22624971 | C2 | semidirect |
| 23. #17988392 | C4 | semidirect |
| 24. #17988390 | C4 | semidirect |
| 25. #17988388 | C4 | semidirect |
| 26. #357×C73 | C4 | semidirect |
| 90. Dic292 | C4⋊C4 | semidirect |
| 103. D8×C73 | C4⋊C4 | semidirect |
| 171. C73 | #12955 | semidirect |
| 189. #357 | #64408 | semidirect |
| 245. D8 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989634 | 2 |
| C2×#17989511 | 2 |
| C2×#17989503 | 2 |
| #22626036 | 2 |
| #22625005 | 2 |
| #22624971 | 2 |
| #22611640 | 2 |
| #12955 | 73 |