Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 132 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. #22626263 | C2 | semidirect |
| 2. C2×#17989485 | C2 | semidirect |
| 3. C2×C4×#11924031 | C2 | semidirect |
| 21. C2×#11924031 | D4 | semidirect |
| 95. C4×C73 | #350 | semidirect |
| 108. C73 | #13191 | semidirect |
| 199. C4 | #17989485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626263 | 2 |
| C2×#17989485 | 2 |
| C2×C4×#11924031 | 2 |
| #22618643 | 2 |
| #13191 | 73 |