Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 124 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×#1136⋊C3 | C2 | semidirect |
| 3. (C22⋊(C7⋊C8))⋊C3 | C2 | semidirect |
| 4. #89979 | C3 | semidirect |
| 12. C2×ΓL(1,𝔽8)⋊C8 | C22 | semidirect |
| 14. C2×#1136 | C2×C3 | semidirect |
| 15. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 36. C2×C7⋊C8 | C22×C3 | semidirect |
| 45. C22×ΓL(1,𝔽8) | M16 | semidirect |
| 83. C22×C7 | C3×M16 | semidirect |
| 100. ΓL(1,𝔽8) | #407 | semidirect |
| 135. C7 | C3×#407 | semidirect |
| 144. C22 | #1136⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×ΓL(1,𝔽8) | 2 |
| C2×#1136⋊C3 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| #89979 | 3 |
| C3×#407 | 7 |