Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×Dic84 | C2 | semidirect |
| 4. C3×C7×#107 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 19. C7×#107 | D3 | semidirect |
| 45. C3×#107 | D7 | semidirect |
| 50. C2×D21 | Q16 | semidirect |
| 84. #107 | D21 | semidirect |
| 106. C3×C7 | #467 | semidirect |
| 140. C7 | #4887 | semidirect |
| 154. C3 | #89659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic84 | 2 |
| C2×C8×D21 | 2 |
| #10621380 | 2 |
| C3×C7×#107 | 2 |
| #10620649 | 2 |
| #89659 | 3 |
| #4887 | 7 |