Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 17. #5092 | C7 | direct (N × H) |
| 38. C3×C4×C7 | Q16 | semidirect |
| 65. C4×C7 | #216 | semidirect |
| 74. C3×C7 | #494 | semidirect |
| 86. C3×C4 | C7×Q16 | semidirect |
| 96. C7 | #5092 | direct (N × H) |
| 102. C4 | C7×#216 | semidirect |
| 104. C3 | C7×#494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊Q8 | 2 |
| C2×C7×#216 | 2 |
| C7×#869 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C7×#494 | 3 |
| #5092 | 7 |