Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
296 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 76 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×#1144 | C2 | semidirect |
| 4. C2×#66569 | C2 | semidirect |
| 5. #10620674 | C2 | semidirect |
| 6. #10620508 | C2 | semidirect |
| 26. C2×#1144 | D3 | semidirect |
| 76. C2×D3×C7 | Q16 | semidirect |
| 160. C3×C7 | #451 | semidirect |
| 183. C2×D3 | #1144 | semidirect |
| 210. C7 | #5186 | semidirect |
| 226. C3 | #90000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×Q8 | 2 |
| C2×C3×#1144 | 2 |
| #10620931 | 2 |
| C2×#66569 | 2 |
| #10620674 | 2 |
| #10620508 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #90000 | 3 |
| #5186 | 7 |