Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
138 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 37 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. #64408⋊C32 | C2 | semidirect |
| 2. #22626997 | C2 | semidirect |
| 19. D1168 | C8 | semidirect |
| 22. D16×C73 | C8 | semidirect |
| 71. C73 | #7383 | semidirect |
| 83. D16 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64408⋊C32 | 2 |
| #22626997 | 2 |
| D16×#64408 | 2 |
| #7383 | 73 |