Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 244 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. C2×C3×#1136 | C2 | semidirect |
| 3. C2×C3×#1131 | C2 | semidirect |
| 4. C3×C7×C22⋊C8 | C2 | semidirect |
| 5. C3×(C2×D7)⋊C8 | C2 | semidirect |
| 6. C3×Dic7⋊C8 | C2 | semidirect |
| 7. C3×C8×Dic7 | C2 | semidirect |
| 8. #89501 | C3 | direct (N × H) |
| 23. C2×#1136 | C2×C3 | semidirect |
| 24. C2×#1131 | C2×C3 | semidirect |
| 25. C7×C22⋊C8 | C2×C3 | semidirect |
| 26. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 27. Dic7⋊C8 | C2×C3 | semidirect |
| 28. C8×Dic7 | C2×C3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 64. C3×C22⋊C8 | D7 | semidirect |
| 78. C3×Dic7 | M16 | semidirect |
| 95. C7⋊C8 | C3×D4 | semidirect |
| 119. C22⋊C8 | C3×D7 | semidirect |
| 133. Dic7 | C3×M16 | semidirect |
| 150. C3×C7 | #436 | semidirect |
| 198. C7 | C3×#436 | semidirect |
| 217. C3 | #89501 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C22⋊D7 | 2 |
| C2×C3×#1136 | 2 |
| C2×C3×#1131 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C3×(C2×D7)⋊C8 | 2 |
| C3×Dic7⋊C8 | 2 |
| C3×C8×Dic7 | 2 |
| #89501 | 3 |
| C3×#436 | 7 |