Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 86 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. C7×#888 | C2 | semidirect |
| 5. C7×#817 | C2 | semidirect |
| 6. C7×Dic3⋊C8 | C2 | semidirect |
| 7. C7×#808 | C2 | semidirect |
| 27. #4761 | C7 | direct (N × H) |
| 30. C3×C7×D4 | Q8 | semidirect |
| 53. #888 | C2×C7 | semidirect |
| 56. #817 | C2×C7 | semidirect |
| 57. Dic3⋊C8 | C2×C7 | semidirect |
| 58. #808 | C2×C7 | semidirect |
| 74. C7×D4 | Dic6 | semidirect |
| 119. C3×D4 | C7×Q8 | semidirect |
| 130. C3×C7 | #476 | semidirect |
| 160. D4 | C7×Dic6 | semidirect |
| 170. C7 | #4761 | direct (N × H) |
| 186. C3 | C7×#476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×Dic3 | 2 |
| C7×#888 | 2 |
| C3×C7×#102 | 2 |
| C7×#832 | 2 |
| C7×#817 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#808 | 2 |
| C7×#476 | 3 |
| #4761 | 7 |