Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
288 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 288 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. #10621423 | C2 | semidirect |
| 2. C2×C7×#214 | C2 | semidirect |
| 3. C2×C3×#1141 | C2 | semidirect |
| 4. #10620930 | C2 | semidirect |
| 5. C2×#66568 | C2 | semidirect |
| 6. C2×#66561 | C2 | semidirect |
| 7. #10620489 | C2 | semidirect |
| 26. C2×#1141 | D3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 46. C7×C3⋊C8 | D4 | semidirect |
| 63. C2×#214 | D7 | semidirect |
| 95. C7⋊C8 | #67 | semidirect |
| 148. C3⋊C8 | C22⋊D7 | semidirect |
| 149. C3×C7 | #496 | semidirect |
| 196. C7 | #5154 | semidirect |
| 213. C3 | #89948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621423 | 2 |
| C2×C7×#214 | 2 |
| C2×C3×#1141 | 2 |
| #10620930 | 2 |
| C2×#66568 | 2 |
| C2×#66561 | 2 |
| #10620489 | 2 |
| #89948 | 3 |
| #5154 | 7 |