Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
676 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 382 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×#217 | C2 | semidirect |
| 3. C7×D4×Dic3 | C2 | semidirect |
| 4. C7×#926 | C2 | semidirect |
| 7. C2×C3×C7×D4 | C4 | semidirect |
| 10. C22×C7×Dic3 | C22 | semidirect |
| 12. C7×#217 | C22 | semidirect |
| 13. C7×C4⋊Dic3 | C22 | semidirect |
| 14. C4×C7×Dic3 | C22 | semidirect |
| 19. #5798 | C7 | direct (N × H) |
| 21. C23×C3×C7 | C2×C4 | semidirect |
| 24. C3×C7×D4 | C2×C4 | semidirect |
| 25. C2×C3×C4×C7 | C2×C4 | semidirect |
| 30. C2×C7×D4 | Dic3 | semidirect |
| 39. C2×#217 | C2×C7 | semidirect |
| 40. D4×Dic3 | C2×C7 | semidirect |
| 41. #926 | C2×C7 | semidirect |
| 52. C23×C7 | C2×Dic3 | semidirect |
| 55. C7×D4 | C2×Dic3 | semidirect |
| 58. C2×C4×C7 | C2×Dic3 | semidirect |
| 61. C2×C3×D4 | C4×C7 | semidirect |
| 64. C22×Dic3 | C22×C7 | semidirect |
| 66. #217 | C22×C7 | semidirect |
| 67. C4⋊Dic3 | C22×C7 | semidirect |
| 68. C4×Dic3 | C22×C7 | semidirect |
| 86. C23×C3 | C2×C4×C7 | semidirect |
| 89. C3×D4 | C2×C4×C7 | semidirect |
| 90. C2×C3×C4 | C2×C4×C7 | semidirect |
| 94. C3×C7 | #518 | semidirect |
| 96. C2×D4 | C7×Dic3 | semidirect |
| 117. C23 | C2×C7×Dic3 | semidirect |
| 120. D4 | C2×C7×Dic3 | semidirect |
| 123. C2×C4 | C2×C7×Dic3 | semidirect |
| 125. C7 | #5798 | direct (N × H) |
| 138. C3 | C7×#518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D4 | 2 |
| C2×C7×#217 | 2 |
| C7×D4×Dic3 | 2 |
| C7×#926 | 2 |
| C7×#518 | 3 |
| #5798 | 7 |