Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 233 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×C4×C7×Q8 | C2 | semidirect |
| 3. Q8×Dic21 | C2 | semidirect |
| 5. #10621370 | C2 | semidirect |
| 7. C4×Dic42 | C2 | semidirect |
| 10. Q8×D21 | C4 | direct (N × H) |
| 23. C4×C7×Q8 | D3 | semidirect |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 40. C4×D21 | Q8 | direct (N × H) |
| 41. Dic42 | C2×C4 | semidirect |
| 56. C3×C4×Q8 | D7 | semidirect |
| 68. C3×C4×C7 | C2×Q8 | semidirect |
| 71. Dic21 | C2×Q8 | semidirect |
| 74. C7×Q8 | C4×D3 | semidirect |
| 101. D21 | C4×Q8 | direct (N × H) |
| 106. C4×Q8 | D21 | direct (N × H) |
| 115. C4×C7 | D3×Q8 | semidirect |
| 120. C3×Q8 | C4×D7 | semidirect |
| 131. C3×C7 | C2×C4×Q8 | semidirect |
| 155. C3×C4 | Q8×D7 | semidirect |
| 161. Q8 | C4×D21 | direct (N × H) |
| 171. C7 | C4×D3×Q8 | semidirect |
| 185. C4 | Q8×D21 | direct (N × H) |
| 186. C3 | C4×Q8×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D21 | 2 |
| C3×C4×C7×Q8 | 2 |
| Q8×Dic21 | 2 |
| C4⋊C4×D21 | 2 |
| #10621370 | 2 |
| C42×D21 | 2 |
| C4×Dic42 | 2 |
| C4×Q8×D7 | 3 |
| C4×D3×Q8 | 7 |