Finite Group DatabasebetaFinite Group DatabasebetaOrder 2688.
688 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 147 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. #13057553 | C2 | semidirect |
| 3. #90012⋊C3 | C2 | semidirect |
| 4. #89987⋊C3 | C2 | semidirect |
| 5. #89326⋊C3 | C2 | semidirect |
| 6. #11729608 | C3 | semidirect |
| 9. ΓL(1,𝔽8)×#127 | C4 | semidirect |
| 10. ΓL(1,𝔽8)×#124 | C4 | semidirect |
| 21. #90510 | C2×C3 | semidirect |
| 22. #90012 | C2×C3 | semidirect |
| 23. #89987 | C2×C3 | semidirect |
| 24. #89326 | C2×C3 | semidirect |
| 50. C2×ΓL(1,𝔽8)⋊C8 | D4 | semidirect |
| 53. C7×#127 | C3×C4 | semidirect |
| 54. C7×#124 | C3×C4 | semidirect |
| 116. C2×C7⋊C8 | C3×D4 | semidirect |
| 206. #127 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 207. #124 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 250. ΓL(1,𝔽8) | #1910 | semidirect |
| 317. C7 | C3×#1910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#535 | 2 |
| #13057553 | 2 |
| #90012⋊C3 | 2 |
| #89987⋊C3 | 2 |
| #89326⋊C3 | 2 |
| #11729608 | 3 |
| C3×#1910 | 7 |