Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 91 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×C4×C7×Q8 | C2 | semidirect |
| 4. #10620674 | C2 | semidirect |
| 6. #10620647 | C2 | semidirect |
| 7. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 16. #66634 | C4 | direct (N × H) |
| 21. C4×C7×Q8 | D3 | semidirect |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 42. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 55. C3×C4×Q8 | D7 | semidirect |
| 69. C3×C4×C7 | SD16 | semidirect |
| 76. C7×Q8 | C4×D3 | semidirect |
| 105. C4×Q8 | D21 | semidirect |
| 118. C4×C7 | #215 | semidirect |
| 124. C3×Q8 | C4×D7 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 160. C3×C4 | #1143 | semidirect |
| 166. Q8 | C4×D21 | semidirect |
| 178. C7 | C4×#215 | semidirect |
| 191. C4 | #66634 | direct (N × H) |
| 194. C3 | C4×#1143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×#66634 | 2 |
| C4×D84 | 2 |
| #10620674 | 2 |
| #10620648 | 2 |
| #10620647 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| C4×#1143 | 3 |
| C4×#215 | 7 |