Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 8. C7×#479 | C3 | semidirect |
| 66. #479 | ΓL(1,𝔽8) | direct (N × H) |
| 119. ΓL(1,𝔽8) | #479 | direct (N × H) |
| 154. C7 | C3×#479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#125 | 2 |
| C4×Q8×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#107 | 2 |
| ΓL(1,𝔽8)×#106 | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| ΓL(1,𝔽8)×#103 | 2 |
| C7×#479 | 3 |
| C3×#479 | 7 |