Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4×#14556687 | C2 | semidirect |
| 3. #22627007 | C2 | semidirect |
| 6. #17989686 | C4 | direct (N × H) |
| 19. #14556687 | C2×C4 | semidirect |
| 142. C4×C73 | #349 | semidirect |
| 145. Dic73 | #349 | semidirect |
| 161. C73 | C4×#349 | semidirect |
| 306. C4 | #17989686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989686 | 2 |
| C4×#14556687 | 2 |
| #22627007 | 2 |
| C2×C4×#11924038 | 2 |
| C4×#349 | 73 |