Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22608844 | C2 | semidirect |
| 3. #22608755 | C2 | semidirect |
| 4. #22607996 | C2 | semidirect |
| 5. #22607899 | C2 | semidirect |
| 6. #22607851 | C2 | semidirect |
| 7. C73×#1333 | C2 | semidirect |
| 60. D8×C73 | M16 | semidirect |
| 114. #1333 | D73 | semidirect |
| 116. C73 | #12078 | semidirect |
| 160. D8 | #11924011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611805 | 2 |
| #22608844 | 2 |
| #22608755 | 2 |
| #22607996 | 2 |
| #22607899 | 2 |
| #22607851 | 2 |
| C73×#1333 | 2 |
| #12078 | 73 |