Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
580 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 267 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 |
|---|---|---|
| 4. #10621352 | C2 | direct (N × H) |
| 20. C2×C3×C4×C7 | Q8 | semidirect |
| 41. C3×C4×C7 | C2×Q8 | semidirect |
| 45. C2×C4×C7 | Dic6 | semidirect |
| 59. C2×C3×C7 | C4⋊Q8 | semidirect |
| 69. C4×C7 | C2×Dic6 | semidirect |
| 73. C2×C3×C4 | Dic14 | semidirect |
| 80. C3×C7 | C2×C4⋊Q8 | semidirect |
| 88. C2×C7 | #869 | semidirect |
| 94. C3×C4 | C2×Dic14 | semidirect |
| 101. C2×C4 | Dic42 | semidirect |
| 105. C7 | C2×#869 | semidirect |
| 106. C2×C3 | #6432 | semidirect |
| 113. C4 | C2×Dic42 | semidirect |
| 115. C3 | C2×#6432 | semidirect |
| 116. C2 | #10621352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C2×C3×C42×C7 | 2 |
| C2×C4⋊Dic21 | 2 |
| #10621352 | 2 |
| C2×#6432 | 3 |
| C2×#869 | 7 |