Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22627133 | C2 | semidirect |
| 2. C4×#14556687 | C2 | semidirect |
| 3. Q8⋊#11924040 | C2 | semidirect |
| 4. D4⋊#11924040 | C2 | semidirect |
| 95. Q8×C73 | M32 | semidirect |
| 98. D4×C73 | M32 | semidirect |
| 152. C73 | #11615 | semidirect |
| 242. Q8 | #14556687 | semidirect |
| 245. D4 | #14556687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627133 | 2 |
| C4×#14556687 | 2 |
| Q8⋊#11924040 | 2 |
| D4⋊#11924040 | 2 |
| #41×#10596833 | 2 |
| #11615 | 73 |