Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 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. C22×C8×ΓL(1,𝔽8) | C2 | semidirect |
| 3. #6489⋊C3 | C2 | semidirect |
| 4. #6395⋊C3 | C2 | semidirect |
| 5. #6390⋊C3 | C2 | semidirect |
| 6. #89885 | C3 | semidirect |
| 10. #1157⋊C3 | C4 | semidirect |
| 20. C22×C7×C8 | C2×C3 | semidirect |
| 21. #6489 | C2×C3 | semidirect |
| 22. #6395 | C2×C3 | semidirect |
| 23. #6390 | C2×C3 | semidirect |
| 43. #1157 | C3×C4 | semidirect |
| 100. C22×C8 | AGL(1,𝔽7) | semidirect |
| 129. ΓL(1,𝔽8) | #416 | semidirect |
| 171. C7 | C3×#416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| C22×C8×ΓL(1,𝔽8) | 2 |
| #6489⋊C3 | 2 |
| #6395⋊C3 | 2 |
| #6390⋊C3 | 2 |
| #89885 | 3 |
| C3×#416 | 7 |