Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 3. C2×Dic3×Dic7 | C2 | semidirect |
| 4. #10620670 | C2 | semidirect |
| 5. C7×C3⋊#95 | C2 | semidirect |
| 13. C2×C3×C4×D7 | C4 | semidirect |
| 14. (C2×D7)⋊Dic3 | C4 | semidirect |
| 32. C2×Dic21 | C2×C4 | semidirect |
| 35. C2×C7×Dic3 | C2×C4 | semidirect |
| 45. C2×C4×D7 | Dic3 | semidirect |
| 52. C3⋊#95 | D7 | semidirect |
| 62. C2×C3×D7 | C42 | semidirect |
| 65. C3×Dic7 | C22⋊C4 | semidirect |
| 114. C2×D7 | C4×Dic3 | semidirect |
| 118. Dic7 | #217 | semidirect |
| 135. C2×Dic3 | C4×D7 | semidirect |
| 136. C3×C7 | C4×C22⋊C4 | semidirect |
| 183. C7 | C4×#217 | semidirect |
| 204. C3 | #89438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D7 | 2 |
| C2×(C2×D7)⋊Dic3 | 2 |
| C2×Dic3×Dic7 | 2 |
| #10620670 | 2 |
| C7×C3⋊#95 | 2 |
| #89438 | 3 |
| C4×#217 | 7 |