Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 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. C4×Dic42 | C2 | semidirect |
| 3. C2×#66570 | C2 | semidirect |
| 5. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 6. #10620506 | C2 | semidirect |
| 64. C4⋊(C3⋊C8) | D7 | semidirect |
| 142. C3×C7 | #464 | semidirect |
| 186. C7 | #5054 | semidirect |
| 202. C3 | #89617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic42 | 2 |
| C3×#6438 | 2 |
| C2×#66570 | 2 |
| C2×#66565 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| #10620506 | 2 |
| #10620500 | 2 |
| #89617 | 3 |
| #5054 | 7 |