Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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. C7×#924 | C2 | semidirect |
| 3. C2×C3×#1136 | C2 | semidirect |
| 4. C2×#66568 | C2 | semidirect |
| 5. #10620523 | C2 | semidirect |
| 6. #10620508 | C2 | semidirect |
| 7. #10620504 | C2 | semidirect |
| 25. C2×#1136 | D3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 61. #924 | D7 | semidirect |
| 95. C7⋊C8 | #67 | semidirect |
| 150. C3×C7 | #468 | semidirect |
| 198. C7 | #5134 | semidirect |
| 217. C3 | #89821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621413 | 2 |
| C7×#924 | 2 |
| C2×C3×#1136 | 2 |
| C2×#66568 | 2 |
| #10620523 | 2 |
| #10620508 | 2 |
| #10620504 | 2 |
| #89821 | 3 |
| #5134 | 7 |