Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 110 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. #22626264 | C2 | semidirect |
| 2. C4×#14556666 | C2 | semidirect |
| 3. #22624882 | C2 | semidirect |
| 4. D4⋊#11924031 | C2 | semidirect |
| 9. C4⋊#11924031 | C22 | semidirect |
| 11. C4×#11924031 | C22 | semidirect |
| 110. D4×C73 | M32 | semidirect |
| 124. D292 | M32 | semidirect |
| 174. C73 | #11583 | semidirect |
| 282. D4 | #14556666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626264 | 2 |
| C4×#14556666 | 2 |
| #22624882 | 2 |
| D4⋊#11924031 | 2 |
| C8×D4×D73 | 2 |
| #11583 | 73 |