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. C4×#14556665 | C2 | semidirect |
| 3. D4⋊#11924031 | C2 | semidirect |
| 8. C4⋊#11924031 | C22 | semidirect |
| 10. C4×#11924031 | C22 | semidirect |
| 89. D4×C73 | M32 | semidirect |
| 137. C73 | #11583 | semidirect |
| 222. D4 | #14556665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626263 | 2 |
| C4×#14556665 | 2 |
| D4⋊#11924031 | 2 |
| C2×D4×#10596831 | 2 |
| #11583 | 73 |