Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
642 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 215 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. #22610653 | C2 | semidirect |
| 4. #22610498 | C2 | semidirect |
| 6. #22610083 | C2 | semidirect |
| 7. C73×#1839 | C2 | semidirect |
| 75. C42×C73 | M16 | semidirect |
| 125. #1839 | D73 | semidirect |
| 126. C73 | #23378 | semidirect |
| 194. C42 | #11924011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556585 | 2 |
| #22610653 | 2 |
| #22610545 | 2 |
| #22610498 | 2 |
| #22610115 | 2 |
| #22610083 | 2 |
| C73×#1839 | 2 |
| #23378 | 73 |