Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 398 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×#17989516 | C2 | semidirect |
| 4. #22626039 | C2 | semidirect |
| 5. #22624992 | C2 | semidirect |
| 6. #22624968 | C2 | semidirect |
| 23. #17988391 | C4 | semidirect |
| 24. #17988389 | C4 | semidirect |
| 25. #17988387 | C4 | semidirect |
| 26. #358×C73 | C4 | semidirect |
| 167. C73 | #12939 | semidirect |
| 183. #358 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989631 | 2 |
| C2×#17989516 | 2 |
| C2×#17989502 | 2 |
| #22626039 | 2 |
| #22624992 | 2 |
| #22624968 | 2 |
| #22611637 | 2 |
| #12939 | 73 |