Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
166 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 29 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. Q8×C22⋊ΓL(1,𝔽8) | C2 | semidirect |
| 3. (C7⋊C8)⋊A4 | C2 | semidirect |
| 4. C22×#1143 | C3 | semidirect |
| 9. C22×C7×Q8 | C2×C3 | semidirect |
| 15. C22×C7⋊C8 | C2×C3 | semidirect |
| 35. #1143 | A4 | semidirect |
| 41. C22⋊ΓL(1,𝔽8) | SD16 | semidirect |
| 54. C7×Q8 | C2×A4 | semidirect |
| 64. C7⋊C8 | C2×A4 | semidirect |
| 71. C22×Q8 | AGL(1,𝔽7) | semidirect |
| 80. C22×C7 | C3×SD16 | semidirect |
| 130. Q8 | D7⋊A4 | semidirect |
| 141. C7 | A4×SD16 | semidirect |
| 152. C22 | #1143⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊ΓL(1,𝔽8) | 2 |
| C4⋊(D7⋊A4) | 2 |
| (C7⋊C8)⋊A4 | 2 |
| C22×#1143 | 3 |
| #1143⋊C3 | 4 |
| A4×SD16 | 7 |