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 |
|---|---|---|
| 1. C7×#944 | C2 | semidirect |
| 5. #10620674 | C2 | semidirect |
| 6. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 7. #10620508 | C2 | semidirect |
| 60. #944 | D7 | semidirect |
| 76. C7×Dic3 | SD16 | semidirect |
| 145. C3×C7 | #461 | semidirect |
| 173. Dic3 | #1143 | semidirect |
| 190. C7 | #5162 | semidirect |
| 206. C3 | #89855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#944 | 2 |
| C2×C3×#1143 | 2 |
| Dic3×D28 | 2 |
| C2×#66563 | 2 |
| #10620674 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620508 | 2 |
| #89855 | 3 |
| #5162 | 7 |