Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 90 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×D3×C7×D4 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C2×C7×D24 | C2 | semidirect |
| 4. C7×#895 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C7×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 16. C2×C7×D12 | C22 | semidirect |
| 18. C2×C3×C7×C8 | C22 | semidirect |
| 19. C3×C7×C4⋊C4 | C22 | semidirect |
| 22. C2×C7×C3⋊C8 | C22 | semidirect |
| 29. C7×#102 | D3 | semidirect |
| 31. #4773 | C7 | direct (N × H) |
| 40. C3×C7×D4 | D4 | semidirect |
| 49. C7×D12 | D4 | semidirect |
| 66. C2×C7×C8 | C2×D3 | semidirect |
| 67. C7×C4⋊C4 | C2×D3 | semidirect |
| 69. C2×D3×D4 | C2×C7 | semidirect |
| 70. C2×#213 | C2×C7 | semidirect |
| 71. C2×D24 | C2×C7 | semidirect |
| 72. #895 | C2×C7 | semidirect |
| 73. C3×#102 | C2×C7 | semidirect |
| 74. (C2×D3)⋊C8 | C2×C7 | semidirect |
| 75. #809 | C2×C7 | semidirect |
| 89. C2×D3×C7 | D8 | semidirect |
| 109. C7×D4 | D12 | semidirect |
| 124. C2×D12 | C22×C7 | semidirect |
| 126. C2×C3×C8 | C22×C7 | semidirect |
| 127. C3×C4⋊C4 | C22×C7 | semidirect |
| 130. C2×C3⋊C8 | C22×C7 | semidirect |
| 144. #102 | D3×C7 | semidirect |
| 172. C3×D4 | C7×D4 | semidirect |
| 181. D12 | C7×D4 | semidirect |
| 186. C3×C7 | #447 | semidirect |
| 199. C2×C8 | C2×D3×C7 | semidirect |
| 200. C4⋊C4 | C2×D3×C7 | semidirect |
| 222. C2×D3 | C7×D8 | semidirect |
| 241. D4 | C7×D12 | semidirect |
| 249. C7 | #4773 | direct (N × H) |
| 275. C3 | C7×#447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×D4 | 2 |
| C2×C7×#213 | 2 |
| C2×C7×D24 | 2 |
| C7×#895 | 2 |
| C3×C7×#102 | 2 |
| C7×(C2×D3)⋊C8 | 2 |
| C7×#809 | 2 |
| C7×#447 | 3 |
| #4773 | 7 |