Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
| 2. C2×#66635 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 7. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 22. C4×C7×Q8 | D3 | semidirect |
| 58. C3×C4×Q8 | D7 | semidirect |
| 112. C4×Q8 | D21 | semidirect |
| 142. C3×C7 | #464 | semidirect |
| 186. C7 | #5028 | semidirect |
| 202. C3 | #89800 | 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×#66635 | 2 |
| C2×#66634 | 2 |
| #10621358 | 2 |
| #10620649 | 2 |
| #10620648 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89800 | 3 |
| #5028 | 7 |