Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
340 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 105 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×C4⋊C4×ΓL(1,𝔽8) | C2 | semidirect |
| 4. ΓL(1,𝔽8)×#95 | C2 | semidirect |
| 5. ΓL(1,𝔽8)×#95 | C2 | semidirect |
| 6. C7×#397 | C3 | semidirect |
| 15. C2×C7×C4⋊C4 | C2×C3 | semidirect |
| 18. C7×#95 | C2×C3 | semidirect |
| 19. C7×#95 | C2×C3 | semidirect |
| 64. #397 | ΓL(1,𝔽8) | direct (N × H) |
| 95. C2×C4⋊C4 | C2×ΓL(1,𝔽8) | semidirect |
| 98. #95 | C2×ΓL(1,𝔽8) | semidirect |
| 99. #95 | C2×ΓL(1,𝔽8) | semidirect |
| 130. ΓL(1,𝔽8) | #397 | direct (N × H) |
| 175. C7 | C3×#397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×ΓL(1,𝔽8) | 2 |
| C2×C22⋊C4×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#95 | 2 |
| C7×#397 | 3 |
| C3×#397 | 7 |