Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 102 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×#877 | C2 | semidirect |
| 3. C3×C7×#99 | C2 | semidirect |
| 4. C7×#834 | C2 | semidirect |
| 5. C7×#806 | C2 | semidirect |
| 8. C2×C7×#67 | C4 | semidirect |
| 10. C22×C7×Dic3 | C4 | semidirect |
| 14. C2×C4×D3×C7 | C4 | semidirect |
| 15. C2×C7×Dic6 | C4 | semidirect |
| 24. C7×#99 | D3 | semidirect |
| 25. #4740 | C7 | direct (N × H) |
| 59. #877 | C2×C7 | semidirect |
| 60. C3×#99 | C2×C7 | semidirect |
| 61. #834 | C2×C7 | semidirect |
| 62. #806 | C2×C7 | semidirect |
| 98. C2×#67 | C4×C7 | semidirect |
| 100. C22×Dic3 | C4×C7 | semidirect |
| 104. C2×C4×D3 | C4×C7 | semidirect |
| 105. C2×Dic6 | C4×C7 | semidirect |
| 119. #99 | D3×C7 | semidirect |
| 153. C3×C7 | #410 | semidirect |
| 205. C7 | #4740 | direct (N × H) |
| 225. C3 | C7×#410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#237 | 2 |
| C7×#877 | 2 |
| C3×C7×#99 | 2 |
| C7×#834 | 2 |
| C7×#806 | 2 |
| C7×#410 | 3 |
| #4740 | 7 |