Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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. C22×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 3. C2×#1132⋊C3 | C2 | semidirect |
| 4. ΓL(1,𝔽8)×C22⋊C8 | C2 | semidirect |
| 5. #6390⋊C3 | C2 | semidirect |
| 6. #89510 | C3 | semidirect |
| 18. C22×Dic14 | C2×C3 | semidirect |
| 20. C2×#1132 | C2×C3 | semidirect |
| 21. C7×C22⋊C8 | C2×C3 | semidirect |
| 22. #6390 | C2×C3 | semidirect |
| 36. ΓL(1,𝔽8)⋊Q8 | D4 | semidirect |
| 56. C22×ΓL(1,𝔽8) | SD16 | semidirect |
| 78. Dic14 | C3×D4 | semidirect |
| 100. C22⋊C8 | AGL(1,𝔽7) | semidirect |
| 103. C22×C7 | C3×SD16 | semidirect |
| 126. ΓL(1,𝔽8) | #448 | semidirect |
| 168. C7 | C3×#448 | semidirect |
| 179. C22 | #1132⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽8)⋊Q8 | 2 |
| #6493⋊C3 | 2 |
| C2×#1132⋊C3 | 2 |
| ΓL(1,𝔽8)×C22⋊C8 | 2 |
| #6390⋊C3 | 2 |
| #89510 | 3 |
| C3×#448 | 7 |