Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
224 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×C4×C7×Q8 | C2 | semidirect |
| 2. C2×C7×#216 | C2 | semidirect |
| 5. C7×#810 | C2 | semidirect |
| 7. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 25. C4×C7×Q8 | D3 | semidirect |
| 29. #5028 | C7 | direct (N × H) |
| 58. C3×C4×Q8 | C2×C7 | semidirect |
| 59. C2×#216 | C2×C7 | semidirect |
| 62. #810 | C2×C7 | semidirect |
| 64. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 112. C4×Q8 | D3×C7 | semidirect |
| 142. C3×C7 | #464 | semidirect |
| 186. C7 | #5028 | direct (N × H) |
| 202. C3 | C7×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×C7×#216 | 2 |
| C2×C7×#215 | 2 |
| C7×#875 | 2 |
| C7×#810 | 2 |
| C7×#809 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#464 | 3 |
| #5028 | 7 |