Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
226 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 28. Dic584 | C8 | semidirect |
| 29. #14556537 | C8 | semidirect |
| 31. Q32×C73 | C8 | semidirect |
| 56. #10596842 | Q32 | direct (N × H) |
| 83. C73 | C8×Q32 | semidirect |
| 98. Q32 | #10596842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#10596842 | 2 |
| #22626997 | 2 |
| #22626978 | 2 |
| C16×#10596842 | 2 |
| Q32×#64408 | 2 |
| C8×Q32 | 73 |