Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
154 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 154 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×Q8×A4 | C2 | semidirect |
| 3. C7×A4⋊C8 | C2 | semidirect |
| 9. C22×C7×Q8 | D3 | semidirect |
| 16. #5417 | C7 | direct (N × H) |
| 36. Q8×A4 | C2×C7 | semidirect |
| 38. A4⋊C8 | C2×C7 | semidirect |
| 40. C7×A4 | SD16 | semidirect |
| 49. C7×Q8 | S4 | semidirect |
| 67. C22×Q8 | D3×C7 | semidirect |
| 79. C22×C7 | #215 | semidirect |
| 110. A4 | C7×SD16 | semidirect |
| 118. Q8 | C7×S4 | semidirect |
| 130. C7 | #5417 | direct (N × H) |
| 138. C22 | C7×#215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×A4 | 2 |
| C7×C4⋊S4 | 2 |
| C7×A4⋊C8 | 2 |
| C7×#448 | 3 |
| C7×#215 | 4 |
| #5417 | 7 |