Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 1. C3×D7×Q16 | C2 | semidirect |
| 3. C3×C7×SD32 | C2 | semidirect |
| 4. C3×#6403 | C2 | semidirect |
| 5. C3×#6401 | C2 | semidirect |
| 6. C3×Dic56 | C2 | semidirect |
| 7. C3×#6372 | C2 | semidirect |
| 8. #89687 | C3 | direct (N × H) |
| 20. D7×Q16 | C2×C3 | semidirect |
| 22. C7×SD32 | C2×C3 | semidirect |
| 23. #6403 | C2×C3 | semidirect |
| 24. #6401 | C2×C3 | semidirect |
| 25. Dic56 | C2×C3 | semidirect |
| 26. #6372 | C2×C3 | semidirect |
| 55. C3×SD32 | D7 | semidirect |
| 95. SD32 | C3×D7 | semidirect |
| 115. C3×C7 | #510 | semidirect |
| 148. C7 | C3×#510 | semidirect |
| 159. C3 | #89687 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D7×Q16 | 2 |
| C3×#6475 | 2 |
| C3×C7×SD32 | 2 |
| C3×#6403 | 2 |
| C3×#6401 | 2 |
| C3×Dic56 | 2 |
| C3×#6372 | 2 |
| #89687 | 3 |
| C3×#510 | 7 |