Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 126 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. C3×C7×#117 | C2 | semidirect |
| 3. C22×C3×C7⋊C8 | C2 | semidirect |
| 4. C3×#6384 | C2 | semidirect |
| 5. C3×#6383 | C2 | semidirect |
| 6. #89774 | C3 | direct (N × H) |
| 10. C3×#1157 | C4 | semidirect |
| 20. C7×#117 | C2×C3 | semidirect |
| 21. C22×C7⋊C8 | C2×C3 | semidirect |
| 22. #6384 | C2×C3 | semidirect |
| 23. #6383 | C2×C3 | semidirect |
| 43. #1157 | C3×C4 | semidirect |
| 54. C3×#117 | D7 | semidirect |
| 101. #117 | C3×D7 | semidirect |
| 129. C3×C7 | #416 | semidirect |
| 171. C7 | C3×#416 | semidirect |
| 186. C3 | #89774 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1157 | 2 |
| C3×C7×#117 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C3×#6384 | 2 |
| C3×#6383 | 2 |
| #89774 | 3 |
| C3×#416 | 7 |