Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 106 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. #6489⋊C3 | C2 | semidirect |
| 3. #6408⋊C3 | C2 | semidirect |
| 4. #90012 | C3 | semidirect |
| 7. C2×Q8×ΓL(1,𝔽8) | C4 | semidirect |
| 8. C2×D4×ΓL(1,𝔽8) | C4 | semidirect |
| 10. C22×C4×ΓL(1,𝔽8) | C4 | semidirect |
| 16. #6489 | C2×C3 | semidirect |
| 17. #6408 | C2×C3 | semidirect |
| 34. C2×C7×Q8 | C3×C4 | semidirect |
| 35. C2×C7×D4 | C3×C4 | semidirect |
| 37. C22×C4×C7 | C3×C4 | semidirect |
| 109. ΓL(1,𝔽8) | #410 | semidirect |
| 112. C2×Q8 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 113. C2×D4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 115. C22×C4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 147. C7 | C3×#410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×ΓL(1,𝔽8) | 2 |
| #6489⋊C3 | 2 |
| #6408⋊C3 | 2 |
| #90012 | 3 |
| C3×#410 | 7 |