Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22626946 | C2 | semidirect |
| 4. C16×#10596842 | C2 | semidirect |
| 19. #14556688 | C8 | semidirect |
| 20. #14556687 | C8 | semidirect |
| 27. #14556666 | C8 | semidirect |
| 28. #14556665 | C8 | semidirect |
| 35. #14556531 | C8 | semidirect |
| 36. #14556530 | C8 | semidirect |
| 38. M32×C73 | C8 | semidirect |
| 42. #11924040 | C2×C8 | semidirect |
| 51. #11924031 | C2×C8 | semidirect |
| 58. #11924003 | C2×C8 | semidirect |
| 60. C16×C73 | C2×C8 | semidirect |
| 66. #10596842 | M32 | direct (N × H) |
| 99. C73 | C8×M32 | semidirect |
| 122. M32 | #10596842 | direct (N × H) |
| 154. C16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64408⋊M32 | 2 |
| C2×C8×#10596842 | 2 |
| #22626946 | 2 |
| C16×#10596842 | 2 |
| M32×#64408 | 2 |
| C8×M32 | 73 |