Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22627117 | C2 | semidirect |
| 2. C4×#14556686 | C2 | semidirect |
| 3. #22626974 | C2 | semidirect |
| 4. D4⋊#11924040 | C2 | semidirect |
| 9. C4⋊#11924040 | C22 | semidirect |
| 11. C4×#11924040 | C22 | semidirect |
| 80. D4×D73 | C16 | semidirect |
| 110. D4×C73 | C2×C16 | semidirect |
| 124. D292 | C2×C16 | semidirect |
| 168. D73 | D4⋊C16 | semidirect |
| 174. C73 | C2×D4⋊C16 | semidirect |
| 282. D4 | #14556686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627117 | 2 |
| C4×#14556686 | 2 |
| #22626974 | 2 |
| D4⋊#11924040 | 2 |
| D4×#11924036 | 2 |
| C2×D4⋊C16 | 73 |