Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#1157⋊C3 | C2 | semidirect |
| 2. ΓL(1,𝔽8)×#121 | C2 | semidirect |
| 3. C2×#1142⋊C3 | C2 | semidirect |
| 4. C2×#1141⋊C3 | C2 | semidirect |
| 5. (C22⋊(C7⋊C8))⋊C3 | C2 | semidirect |
| 6. #6384⋊C3 | C2 | semidirect |
| 7. #6383⋊C3 | C2 | semidirect |
| 8. #89809 | C3 | semidirect |
| 24. C2×#1157 | C2×C3 | semidirect |
| 25. C7×#121 | C2×C3 | semidirect |
| 26. C2×#1142 | C2×C3 | semidirect |
| 27. C2×#1141 | C2×C3 | semidirect |
| 28. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 29. #6384 | C2×C3 | semidirect |
| 30. #6383 | C2×C3 | semidirect |
| 46. C4⋊AGL(1,𝔽7) | D4 | semidirect |
| 49. ΓL(1,𝔽8)⋊Q8 | D4 | semidirect |
| 104. D28 | C3×D4 | semidirect |
| 107. Dic14 | C3×D4 | semidirect |
| 134. #121 | AGL(1,𝔽7) | semidirect |
| 173. ΓL(1,𝔽8) | #449 | semidirect |
| 230. C7 | C3×#449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| ΓL(1,𝔽8)×#121 | 2 |
| C2×#1142⋊C3 | 2 |
| C2×#1141⋊C3 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| #6384⋊C3 | 2 |
| #6383⋊C3 | 2 |
| #89809 | 3 |
| C3×#449 | 7 |