Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 4. #10620489 | C2 | semidirect |
| 5. #10620486 | C2 | semidirect |
| 11. C2×C7×C3⋊C8 | C4 | semidirect |
| 14. C3×#1136 | C4 | semidirect |
| 38. #1136 | Dic3 | semidirect |
| 68. C2×C3⋊C8 | Dic7 | semidirect |
| 95. C3×C7 | #405 | semidirect |
| 124. C7 | #5122 | semidirect |
| 135. C3 | #89873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621409 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C2×C3×#1136 | 2 |
| #10620489 | 2 |
| #10620486 | 2 |
| #89873 | 3 |
| #5122 | 7 |