Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
644 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 138 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×C7×D4 | C2 | semidirect |
| 2. C22×C7×#67 | C2 | semidirect |
| 3. C2×C7×#217 | C2 | semidirect |
| 4. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C7×C3⋊#95 | C2 | semidirect |
| 20. C22×C7×D4 | D3 | semidirect |
| 24. #5223 | C7 | direct (N × H) |
| 31. C23×C3×C7 | D4 | semidirect |
| 37. C22×D3×C7 | D4 | semidirect |
| 40. C2×C3×C4×C7 | D4 | semidirect |
| 46. C2×C7×Dic3 | D4 | semidirect |
| 59. C22×C3×D4 | C2×C7 | semidirect |
| 60. C22×#67 | C2×C7 | semidirect |
| 61. C2×#217 | C2×C7 | semidirect |
| 62. C2×(C2×D3)⋊C4 | C2×C7 | semidirect |
| 63. C3⋊#95 | C2×C7 | semidirect |
| 96. C23×C7 | #67 | semidirect |
| 106. C2×C4×C7 | #67 | semidirect |
| 127. C22×D4 | D3×C7 | semidirect |
| 157. C23×C3 | C7×D4 | semidirect |
| 163. C22×D3 | C7×D4 | semidirect |
| 166. C2×C3×C4 | C7×D4 | semidirect |
| 172. C2×Dic3 | C7×D4 | semidirect |
| 173. C3×C7 | #392 | semidirect |
| 224. C23 | C7×#67 | semidirect |
| 234. C2×C4 | C7×#67 | semidirect |
| 235. C7 | #5223 | direct (N × H) |
| 263. C3 | C7×#392 | 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 |
| C22×C7×#67 | 2 |
| C2×C7×#217 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#392 | 3 |
| #5223 | 7 |