Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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×C4⋊C4×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C2×C22⋊C4×ΓL(1,𝔽8) | C2 | semidirect |
| 4. C2×C22⋊C4×ΓL(1,𝔽8) | C2 | semidirect |
| 5. ΓL(1,𝔽8)×#95 | C2 | semidirect |
| 6. C7×#394 | C3 | semidirect |
| 18. C2×C7×C4⋊C4 | C2×C3 | semidirect |
| 19. C2×C7×C22⋊C4 | C2×C3 | semidirect |
| 20. C2×C7×C22⋊C4 | C2×C3 | semidirect |
| 21. C7×#95 | C2×C3 | semidirect |
| 41. C2×C4×ΓL(1,𝔽8) | D4 | semidirect |
| 73. #394 | ΓL(1,𝔽8) | direct (N × H) |
| 92. C2×C4×C7 | C3×D4 | semidirect |
| 110. C2×C4⋊C4 | C2×ΓL(1,𝔽8) | semidirect |
| 111. C2×C22⋊C4 | C2×ΓL(1,𝔽8) | semidirect |
| 112. C2×C22⋊C4 | C2×ΓL(1,𝔽8) | semidirect |
| 113. #95 | C2×ΓL(1,𝔽8) | semidirect |
| 149. ΓL(1,𝔽8) | #394 | direct (N × H) |
| 200. C2×C4 | D4×ΓL(1,𝔽8) | semidirect |
| 201. C7 | C3×#394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×ΓL(1,𝔽8) | 2 |
| C2×C4⋊C4×ΓL(1,𝔽8) | 2 |
| C2×C22⋊C4×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#95 | 2 |
| C7×#394 | 3 |
| C3×#394 | 7 |