Finite Group DatabasebetaFinite Group DatabasebetaOrder 2688.
252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #89452⋊C3 | C2 | semidirect |
| 4. #89289⋊C3 | C2 | semidirect |
| 5. #89258⋊C3 | C2 | semidirect |
| 6. #11728673 | C3 | semidirect |
| 17. #89452 | C2×C3 | semidirect |
| 19. #89289 | C2×C3 | semidirect |
| 20. #89258 | C2×C3 | semidirect |
| 24. Q16×ΓL(1,𝔽8) | Q8 | semidirect |
| 26. D8×ΓL(1,𝔽8) | Q8 | semidirect |
| 66. C7×Q16 | C3×Q8 | semidirect |
| 68. C7×D8 | C3×Q8 | semidirect |
| 158. ΓL(1,𝔽8) | #2230 | semidirect |
| 161. Q16 | ΓL(1,𝔽8)⋊Q8 | semidirect |
| 163. D8 | ΓL(1,𝔽8)⋊Q8 | semidirect |
| 196. C7 | C3×#2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#443 | 2 |
| #89452⋊C3 | 2 |
| #89361⋊C3 | 2 |
| #89289⋊C3 | 2 |
| #89258⋊C3 | 2 |
| #11728673 | 3 |
| C3×#2230 | 7 |