Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14556531 | C2 | semidirect |
| 3. #22607912 | C2 | semidirect |
| 4. #22607888 | C2 | semidirect |
| 5. C73×#2163 | C2 | semidirect |
| 140. #2163 | D73 | semidirect |
| 144. C73 | #11620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618906 | 2 |
| C4×#14556531 | 2 |
| #22607912 | 2 |
| #22607888 | 2 |
| C73×#2163 | 2 |
| #11620 | 73 |