Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
174 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 30 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. C7×D4×A4 | C2 | semidirect |
| 2. C7×C4⋊S4 | C2 | semidirect |
| 3. C7×A4⋊C8 | C2 | semidirect |
| 9. C22×C7×D4 | D3 | semidirect |
| 16. #5415 | C7 | direct (N × H) |
| 37. D4×A4 | C2×C7 | semidirect |
| 38. C4⋊S4 | C2×C7 | semidirect |
| 39. A4⋊C8 | C2×C7 | semidirect |
| 42. C7×A4 | D8 | semidirect |
| 58. C7×D4 | S4 | semidirect |
| 71. C22×D4 | D3×C7 | semidirect |
| 89. C22×C7 | #213 | semidirect |
| 122. A4 | C7×D8 | semidirect |
| 137. D4 | C7×S4 | semidirect |
| 143. C7 | #5415 | direct (N × H) |
| 158. C22 | C7×#213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×A4 | 2 |
| C7×C4⋊S4 | 2 |
| C7×A4⋊C8 | 2 |
| C7×#447 | 3 |
| C7×#213 | 4 |
| #5415 | 7 |