Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10620900 | C2 | semidirect |
| 3. C2×D3×C7⋊C8 | C2 | semidirect |
| 4. #10620671 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. #10620508 | C2 | semidirect |
| 7. #10620507 | C2 | semidirect |
| 13. C7×#237 | C4 | semidirect |
| 29. #6406 | D3 | semidirect |
| 104. #237 | Dic7 | semidirect |
| 156. C3×C7 | #416 | semidirect |
| 206. C7 | #4772 | semidirect |
| 225. C3 | #90005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#237 | 2 |
| #10620900 | 2 |
| C2×D3×C7⋊C8 | 2 |
| #10620671 | 2 |
| C3×#6406 | 2 |
| #10620508 | 2 |
| #10620507 | 2 |
| #90005 | 3 |
| #4772 | 7 |