Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 1. #22626320 | C2 | semidirect |
| 2. #22626318 | C2 | semidirect |
| 3. #22624967 | C2 | semidirect |
| 4. #22624894 | C2 | semidirect |
| 5. #22624893 | C2 | semidirect |
| 6. C16×#10596833 | C2 | semidirect |
| 35. #14556537 | C8 | semidirect |
| 36. #14556535 | C8 | semidirect |
| 37. #14556534 | C8 | semidirect |
| 38. #14556532 | C8 | semidirect |
| 110. C73 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626320 | 2 |
| #22626318 | 2 |
| #22624967 | 2 |
| #22624894 | 2 |
| #22624893 | 2 |
| C16×#10596833 | 2 |
| #22611809 | 2 |
| #12046 | 73 |