Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 2. C2×C7×ΓL(1,𝔽25) | C2 | semidirect |
| 3. D3×C7×C4⋊C4 | C2 | semidirect |
| 4. C3×C7×#102 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 6. C7×#816 | C2 | semidirect |
| 7. C7×#810 | C2 | semidirect |
| 13. C7×#237 | C4 | semidirect |
| 29. C7×#102 | D3 | semidirect |
| 30. #4771 | C7 | direct (N × H) |
| 34. C3×C7×D4 | C2×C4 | semidirect |
| 46. C7×Dic6 | C2×C4 | semidirect |
| 64. C2×ΓL(1,𝔽25) | C2×C7 | semidirect |
| 65. D3×C4⋊C4 | C2×C7 | semidirect |
| 66. C3×#102 | C2×C7 | semidirect |
| 67. #832 | C2×C7 | semidirect |
| 68. #816 | C2×C7 | semidirect |
| 69. #810 | C2×C7 | semidirect |
| 90. C7×D4 | C4×D3 | semidirect |
| 106. #237 | C4×C7 | semidirect |
| 127. #102 | D3×C7 | semidirect |
| 144. C3×D4 | C2×C4×C7 | semidirect |
| 156. Dic6 | C2×C4×C7 | semidirect |
| 159. C3×C7 | #417 | semidirect |
| 198. D4 | C4×D3×C7 | semidirect |
| 210. C7 | #4771 | direct (N × H) |
| 229. C3 | C7×#417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#237 | 2 |
| C2×C7×ΓL(1,𝔽25) | 2 |
| D3×C7×C4⋊C4 | 2 |
| C3×C7×#102 | 2 |
| C7×#832 | 2 |
| C7×#816 | 2 |
| C7×#810 | 2 |
| C7×#417 | 3 |
| #4771 | 7 |