Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. C2×Q16×ΓL(1,𝔽8) | C2 | semidirect |
| 3. #6403⋊C3 | C2 | semidirect |
| 4. #6402⋊C3 | C2 | semidirect |
| 5. #6386⋊C3 | C2 | semidirect |
| 6. #89951 | C3 | semidirect |
| 16. C2×C7×Q16 | C2×C3 | semidirect |
| 18. #6403 | C2×C3 | semidirect |
| 19. #6402 | C2×C3 | semidirect |
| 20. #6386 | C2×C3 | semidirect |
| 76. C2×Q16 | AGL(1,𝔽7) | semidirect |
| 96. ΓL(1,𝔽8) | #510 | semidirect |
| 125. C7 | C3×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×ΓL(1,𝔽8) | 2 |
| #6467⋊C3 | 2 |
| #6403⋊C3 | 2 |
| #6402⋊C3 | 2 |
| #6386⋊C3 | 2 |
| #89951 | 3 |
| C3×#510 | 7 |