Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 156 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. C2×C4⋊#11924031 | C2 | semidirect |
| 2. C2×#17989482 | C2 | semidirect |
| 3. C2×C4×#11924031 | C2 | semidirect |
| 21. C2×#11924031 | D4 | semidirect |
| 45. C2×D292 | C16 | semidirect |
| 106. C4×C73 | C22⋊C16 | semidirect |
| 122. C73 | #13189 | semidirect |
| 225. C4 | #17989482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11924031 | 2 |
| C2×#17989482 | 2 |
| C2×C4×#11924031 | 2 |
| C2×#17988652 | 2 |
| #13189 | 73 |