Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
522 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22609967 | C2 | semidirect |
| 3. C22⋊C4×#10596831 | C2 | semidirect |
| 4. #22608450 | C2 | semidirect |
| 5. #22608296 | C2 | semidirect |
| 8. C22×#11924016 | C4 | semidirect |
| 16. C2×#14556522 | C4 | semidirect |
| 17. C2×#14556514 | C4 | semidirect |
| 18. C2×#14556512 | C4 | semidirect |
| 223. C73 | #9813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988814 | 2 |
| #22609967 | 2 |
| C22⋊C4×#10596831 | 2 |
| #22608450 | 2 |
| #22608296 | 2 |
| #22608291 | 2 |
| C73×#1507 | 2 |
| #9813 | 73 |