Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 78 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×#6507 | C2 | semidirect |
| 3. C3×#6472 | C2 | semidirect |
| 4. C3×C7×#101 | C2 | semidirect |
| 5. C3×#6399 | C2 | semidirect |
| 6. #89524 | C3 | direct (N × H) |
| 19. #6507 | C2×C3 | semidirect |
| 20. #6472 | C2×C3 | semidirect |
| 21. C7×#101 | C2×C3 | semidirect |
| 22. #6399 | C2×C3 | semidirect |
| 53. C3×#101 | D7 | semidirect |
| 94. #101 | C3×D7 | semidirect |
| 116. C3×C7 | #456 | semidirect |
| 152. C7 | C3×#456 | semidirect |
| 163. C3 | #89524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6551 | 2 |
| C3×#6507 | 2 |
| C3×#6472 | 2 |
| C3×C7×#101 | 2 |
| C3×#6399 | 2 |
| #89524 | 3 |
| C3×#456 | 7 |