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. #10621419 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C2×C3×#1141 | C2 | semidirect |
| 4. #10621025 | C2 | semidirect |
| 5. C2×#66567 | C2 | semidirect |
| 6. C2×#66565 | C2 | semidirect |
| 7. #10620489 | C2 | semidirect |
| 26. C2×#1141 | D3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 46. C7×C3⋊C8 | D4 | semidirect |
| 64. C2×#213 | D7 | semidirect |
| 95. C7⋊C8 | #67 | semidirect |
| 148. C3⋊C8 | C22⋊D7 | semidirect |
| 149. C3×C7 | #496 | semidirect |
| 196. C7 | #5154 | semidirect |
| 213. C3 | #89926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621419 | 2 |
| C2×C7×#213 | 2 |
| C2×C3×#1141 | 2 |
| #10621025 | 2 |
| C2×#66567 | 2 |
| C2×#66565 | 2 |
| #10620489 | 2 |
| #89926 | 3 |
| #5154 | 7 |