Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 3. #22624842 | C2 | semidirect |
| 4. C16×#10596833 | C2 | semidirect |
| 19. #14556666 | C8 | semidirect |
| 27. #14556530 | C8 | semidirect |
| 37. #11924031 | C2×C8 | semidirect |
| 46. #11924003 | C2×C8 | semidirect |
| 50. C16×C73 | C2×C8 | semidirect |
| 60. #10596833 | M32 | semidirect |
| 82. C73 | C8×M32 | semidirect |
| 127. C16 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626138 | 2 |
| C8×#11924036 | 2 |
| #22624842 | 2 |
| C16×#10596833 | 2 |
| #22611524 | 2 |
| C8×M32 | 73 |