Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. ΓL(1,𝔽8)×#108 | C2 | direct (N × H) |
| 4. C2×C7×#108 | C3 | semidirect |
| 14. C7×#108 | C2×C3 | semidirect |
| 43. C2×#108 | ΓL(1,𝔽8) | direct (N × H) |
| 62. C2×ΓL(1,𝔽8) | #108 | direct (N × H) |
| 66. #108 | C2×ΓL(1,𝔽8) | direct (N × H) |
| 84. ΓL(1,𝔽8) | C2×#108 | direct (N × H) |
| 94. C2×C7 | C3×#108 | semidirect |
| 113. C7 | C2×C3×#108 | semidirect |
| 129. C2 | ΓL(1,𝔽8)×#108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×ΓL(1,𝔽8) | 2 |
| C22×C8×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#108 | 2 |
| C2×C7×#108 | 3 |
| C2×C3×#108 | 7 |