Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 1. C22×C3×C7×Q8 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 5. C7×#830 | C2 | semidirect |
| 18. C22×C7×Q8 | D3 | semidirect |
| 23. #5227 | C7 | direct (N × H) |
| 28. C3×C7×Q8 | D4 | semidirect |
| 49. C22×C3×Q8 | C2×C7 | semidirect |
| 50. C2×#215 | C2×C7 | semidirect |
| 52. #835 | C2×C7 | semidirect |
| 53. #830 | C2×C7 | semidirect |
| 56. C22×C3×C7 | SD16 | semidirect |
| 70. C7×Q8 | #67 | semidirect |
| 96. C22×Q8 | D3×C7 | semidirect |
| 106. C22×C7 | #215 | semidirect |
| 116. C3×Q8 | C7×D4 | semidirect |
| 126. C3×C7 | #448 | semidirect |
| 145. C22×C3 | C7×SD16 | semidirect |
| 158. Q8 | C7×#67 | semidirect |
| 168. C7 | #5227 | direct (N × H) |
| 179. C22 | C7×#215 | semidirect |
| 185. C3 | C7×#448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C2×C7×#215 | 2 |
| C7×#930 | 2 |
| C7×#835 | 2 |
| C7×#830 | 2 |
| C7×#448 | 3 |
| #5227 | 7 |