Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
174 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 40 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×#41⋊ΓL(1,𝔽8) | C2 | semidirect |
| 2. C4×C7⋊SL(2,𝔽3) | C2 | semidirect |
| 3. C7×#550 | C3 | semidirect |
| 13. C7⋊SL(2,𝔽3) | D4 | semidirect |
| 32. #550 | ΓL(1,𝔽8) | semidirect |
| 65. C4×C7 | #41⋊C3 | semidirect |
| 101. C7 | C4⋊(#41⋊C3) | semidirect |
| 113. C4 | #41⋊ΓL(1,𝔽8) | 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 |
| C4×C7⋊SL(2,𝔽3) | 2 |
| C7×#550 | 3 |
| C4⋊C4×ΓL(1,𝔽8) | 4 |
| C4⋊(#41⋊C3) | 7 |