Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 380 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. C7×#892 | C2 | semidirect |
| 4. C3×C7×#102 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 6. C7×#821 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 13. D3×C7×D4 | C4 | semidirect |
| 16. C2×C3×C7×C8 | C22 | semidirect |
| 17. C3×C7×C4⋊C4 | C22 | semidirect |
| 19. C7×C4⋊Dic3 | C22 | semidirect |
| 21. C2×C7×C3⋊C8 | C22 | semidirect |
| 29. C7×#102 | D3 | semidirect |
| 30. #4770 | C7 | direct (N × H) |
| 59. C2×C7×C8 | C2×D3 | semidirect |
| 61. C7×C4⋊C4 | C2×D3 | semidirect |
| 65. C2×ΓL(1,𝔽25) | C2×C7 | semidirect |
| 66. #892 | C2×C7 | semidirect |
| 67. C3×#102 | C2×C7 | semidirect |
| 68. #832 | C2×C7 | semidirect |
| 69. #821 | C2×C7 | semidirect |
| 70. #809 | C2×C7 | semidirect |
| 111. D3×D4 | C4×C7 | semidirect |
| 114. C2×C3×C8 | C22×C7 | semidirect |
| 115. C3×C4⋊C4 | C22×C7 | semidirect |
| 117. C4⋊Dic3 | C22×C7 | semidirect |
| 119. C2×C3⋊C8 | C22×C7 | semidirect |
| 133. #102 | D3×C7 | semidirect |
| 169. C3×C7 | #418 | semidirect |
| 179. C2×C8 | C2×D3×C7 | semidirect |
| 181. C4⋊C4 | C2×D3×C7 | semidirect |
| 225. C7 | #4770 | direct (N × H) |
| 248. C3 | C7×#418 | 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×ΓL(1,𝔽25) | 2 |
| C7×#892 | 2 |
| C3×C7×#102 | 2 |
| C7×#832 | 2 |
| C7×#821 | 2 |
| C7×#809 | 2 |
| C7×#418 | 3 |
| #4770 | 7 |