Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 316 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×D3×C7×C8 | C2 | semidirect |
| 3. C7×#892 | C2 | semidirect |
| 4. C3×C7×#102 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 6. C7×#816 | C2 | semidirect |
| 7. C7×#810 | C2 | semidirect |
| 13. C7×#237 | C4 | semidirect |
| 29. C7×#102 | D3 | semidirect |
| 30. #4772 | C7 | direct (N × H) |
| 63. C2×D3×C8 | C2×C7 | semidirect |
| 64. #892 | C2×C7 | semidirect |
| 65. C3×#102 | C2×C7 | semidirect |
| 66. #832 | C2×C7 | semidirect |
| 67. #816 | C2×C7 | semidirect |
| 68. #810 | C2×C7 | semidirect |
| 104. #237 | C4×C7 | semidirect |
| 125. #102 | D3×C7 | semidirect |
| 156. C3×C7 | #416 | semidirect |
| 206. C7 | #4772 | direct (N × H) |
| 225. C3 | C7×#416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#237 | 2 |
| C2×D3×C7×C8 | 2 |
| C7×#892 | 2 |
| C3×C7×#102 | 2 |
| C7×#832 | 2 |
| C7×#816 | 2 |
| C7×#810 | 2 |
| C7×#416 | 3 |
| #4772 | 7 |