Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 126 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×C3×C7×C4⋊C4 | C2 | semidirect |
| 3. C2×C3×#1136 | C2 | semidirect |
| 4. C3×#6384 | C2 | semidirect |
| 5. C3×#6383 | C2 | semidirect |
| 6. #89738 | C3 | direct (N × H) |
| 11. C3×#1157 | C4 | semidirect |
| 20. C2×C7×C4⋊C4 | C2×C3 | semidirect |
| 21. C2×#1136 | C2×C3 | semidirect |
| 22. #6384 | C2×C3 | semidirect |
| 23. #6383 | C2×C3 | semidirect |
| 36. C3×D28 | C2×C4 | semidirect |
| 39. C3×Dic14 | C2×C4 | semidirect |
| 45. #1157 | C3×C4 | semidirect |
| 55. C2×C3×C4⋊C4 | D7 | semidirect |
| 82. D28 | C2×C3×C4 | semidirect |
| 85. Dic14 | C2×C3×C4 | semidirect |
| 106. C2×C4⋊C4 | C3×D7 | semidirect |
| 137. C3×C7 | #417 | semidirect |
| 183. C7 | C3×#417 | semidirect |
| 201. C3 | #89738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1157 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C2×C3×#1136 | 2 |
| C3×#6384 | 2 |
| C3×#6383 | 2 |
| #89738 | 3 |
| C3×#417 | 7 |