Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22626806 | C2 | semidirect |
| 2. #22625318 | C2 | semidirect |
| 3. C2×#17989439 | C2 | semidirect |
| 4. #22625208 | C2 | semidirect |
| 5. #22624814 | C2 | semidirect |
| 6. #22624768 | C2 | semidirect |
| 27. #17988905 | C4 | semidirect |
| 30. #17988737 | C4 | semidirect |
| 32. #17988723 | C4 | semidirect |
| 34. #484×C73 | C4 | semidirect |
| 253. C73 | #9264 | semidirect |
| 256. #484 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626806 | 2 |
| #22625318 | 2 |
| C2×#17989439 | 2 |
| #22625208 | 2 |
| #22624814 | 2 |
| #22624768 | 2 |
| #22620701 | 2 |
| #9264 | 73 |