Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
468 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 120 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×#66577 | C2 | semidirect |
| 4. C7×C3⋊#95 | C2 | semidirect |
| 5. C3×C7⋊#95 | C2 | semidirect |
| 11. C2×C4×D21 | C4 | semidirect |
| 20. C7⋊#95 | D3 | semidirect |
| 52. C3⋊#95 | D7 | semidirect |
| 62. C2×D21 | C4⋊C4 | semidirect |
| 64. Dic21 | C22⋊C4 | semidirect |
| 136. C3×C7 | #380 | semidirect |
| 183. C7 | #4667 | semidirect |
| 204. C3 | #89439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C2×#66577 | 2 |
| C2×#66575 | 2 |
| C7×C3⋊#95 | 2 |
| C3×C7⋊#95 | 2 |
| #89439 | 3 |
| #4667 | 7 |