Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
224 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 68 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. C2×#66635 | C2 | semidirect |
| 2. C7×Q8×Dic3 | C2 | semidirect |
| 5. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 6. #10620510 | C2 | semidirect |
| 59. Q8×Dic3 | D7 | semidirect |
| 142. C3×C7 | #464 | semidirect |
| 186. C7 | #5166 | semidirect |
| 202. C3 | #89800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66635 | 2 |
| C7×Q8×Dic3 | 2 |
| C2×C3×#1143 | 2 |
| #10620926 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620510 | 2 |
| #10620499 | 2 |
| #89800 | 3 |
| #5166 | 7 |