Finite Group DatabasebetaFinite Group DatabasebetaOrder 2688.
1640 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×#6407⋊C3 | C2 | semidirect |
| 3. #89979⋊C3 | C2 | semidirect |
| 4. #11729883 | C3 | semidirect |
| 11. C2×#1136⋊C3 | C22 | semidirect |
| 15. C2×#6407 | C2×C3 | semidirect |
| 16. #89979 | C2×C3 | semidirect |
| 41. C2×#1136 | C22×C3 | semidirect |
| 103. C22×ΓL(1,𝔽8) | #100 | semidirect |
| 171. C22×C7 | C3×#100 | semidirect |
| 196. ΓL(1,𝔽8) | #1783 | semidirect |
| 253. C7 | C3×#1783 | semidirect |
| 268. C22 | #6407⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×ΓL(1,𝔽8) | 2 |
| C2×#6407⋊C3 | 2 |
| #89979⋊C3 | 2 |
| #11729883 | 3 |
| C3×#1783 | 7 |