Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×C3×C7×#41 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 3. C2×C7×#213 | C2 | semidirect |
| 4. C7×#930 | C2 | semidirect |
| 5. C7×#835 | C2 | semidirect |
| 6. C7×#832 | C2 | semidirect |
| 7. C7×#830 | C2 | semidirect |
| 24. C2×C7×#41 | D3 | semidirect |
| 31. #5238 | C7 | direct (N × H) |
| 36. C3×C7×Q8 | D4 | semidirect |
| 39. C3×C7×D4 | D4 | semidirect |
| 67. C2×C3×#41 | C2×C7 | semidirect |
| 68. C2×#215 | C2×C7 | semidirect |
| 69. C2×#213 | C2×C7 | semidirect |
| 70. #930 | C2×C7 | semidirect |
| 71. #835 | C2×C7 | semidirect |
| 72. #832 | C2×C7 | semidirect |
| 73. #830 | C2×C7 | semidirect |
| 94. C7×Q8 | #67 | semidirect |
| 100. C7×D4 | #67 | semidirect |
| 131. C2×#41 | D3×C7 | semidirect |
| 157. C3×Q8 | C7×D4 | semidirect |
| 160. C3×D4 | C7×D4 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 214. Q8 | C7×#67 | semidirect |
| 220. D4 | C7×#67 | semidirect |
| 230. C7 | #5238 | direct (N × H) |
| 252. C3 | C7×#449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#41 | 2 |
| C2×C7×#215 | 2 |
| C2×C7×#213 | 2 |
| C7×#930 | 2 |
| C7×#835 | 2 |
| C7×#832 | 2 |
| C7×#830 | 2 |
| C7×#449 | 3 |
| #5238 | 7 |