Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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×#214 | C2 | semidirect |
| 3. C2×D3×C7×C8 | C2 | semidirect |
| 4. C7×#897 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C7×#816 | C2 | semidirect |
| 7. C7×#808 | C2 | semidirect |
| 28. C7×#102 | D3 | semidirect |
| 29. #4778 | C7 | direct (N × H) |
| 45. C7×C3⋊C8 | D4 | semidirect |
| 60. C2×#214 | C2×C7 | semidirect |
| 61. C2×D3×C8 | C2×C7 | semidirect |
| 62. #897 | C2×C7 | semidirect |
| 63. C3×#102 | C2×C7 | semidirect |
| 64. #816 | C2×C7 | semidirect |
| 65. #808 | C2×C7 | semidirect |
| 72. C2×D3×C7 | SD16 | semidirect |
| 120. #102 | D3×C7 | semidirect |
| 149. C3⋊C8 | C7×D4 | semidirect |
| 150. C3×C7 | #465 | semidirect |
| 175. C2×D3 | C7×SD16 | semidirect |
| 198. C7 | #4778 | direct (N × H) |
| 217. C3 | C7×#465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#938 | 2 |
| C2×C7×#214 | 2 |
| C2×D3×C7×C8 | 2 |
| C7×#897 | 2 |
| C3×C7×#102 | 2 |
| C7×#816 | 2 |
| C7×#808 | 2 |
| C7×#465 | 3 |
| #4778 | 7 |