Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
644 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 134 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. C22×C3×C22⋊D7 | C2 | semidirect |
| 2. C22×C3×D28 | C2 | semidirect |
| 3. C2×C3×C7×C22⋊C4 | C2 | semidirect |
| 4. C2×C3×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C3×C7⋊#95 | C2 | semidirect |
| 6. #89732 | C3 | direct (N × H) |
| 19. C22×C22⋊D7 | C2×C3 | semidirect |
| 20. C22×D28 | C2×C3 | semidirect |
| 21. C2×C7×C22⋊C4 | C2×C3 | semidirect |
| 22. C2×(C2×D7)⋊C4 | C2×C3 | semidirect |
| 23. C7⋊#95 | C2×C3 | semidirect |
| 29. C23×C3×C7 | D4 | semidirect |
| 37. C22×C3×D7 | D4 | semidirect |
| 41. C2×C3×C4×C7 | D4 | semidirect |
| 45. C2×C3×Dic7 | D4 | semidirect |
| 62. C2×C3×C22⋊C4 | D7 | semidirect |
| 89. C23×C7 | C3×D4 | semidirect |
| 97. C22×D7 | C3×D4 | semidirect |
| 101. C2×C4×C7 | C3×D4 | semidirect |
| 105. C2×Dic7 | C3×D4 | semidirect |
| 129. C2×C22⋊C4 | C3×D7 | semidirect |
| 162. C23×C3 | D28 | semidirect |
| 172. C2×C3×C4 | C22⋊D7 | semidirect |
| 173. C3×C7 | #392 | semidirect |
| 224. C23 | C3×D28 | semidirect |
| 234. C2×C4 | C3×C22⋊D7 | semidirect |
| 235. C7 | C3×#392 | semidirect |
| 263. C3 | #89732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊D7 | 2 |
| C22×C3×D28 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×C3×(C2×D7)⋊C4 | 2 |
| C3×C7⋊#95 | 2 |
| #89732 | 3 |
| C3×#392 | 7 |