Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. C3×C7×#103 | C2 | semidirect |
| 5. #10620674 | C2 | semidirect |
| 6. #10620655 | C2 | semidirect |
| 7. #10620649 | C2 | semidirect |
| 11. Q8×D21 | C4 | semidirect |
| 26. C7×#103 | D3 | semidirect |
| 33. C3×C7×Q8 | C2×C4 | semidirect |
| 46. Dic42 | C2×C4 | semidirect |
| 66. C3×#103 | D7 | semidirect |
| 84. C7×Q8 | C4×D3 | semidirect |
| 117. D21 | #103 | direct (N × H) |
| 124. #103 | D21 | direct (N × H) |
| 138. C3×Q8 | C4×D7 | semidirect |
| 154. C3×C7 | C2×#103 | semidirect |
| 189. Q8 | C4×D21 | semidirect |
| 202. C7 | D3×#103 | semidirect |
| 218. C3 | D7×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D21 | 2 |
| C2×C8×D21 | 2 |
| C4⋊C4×D21 | 2 |
| C3×C7×#103 | 2 |
| #10620674 | 2 |
| #10620655 | 2 |
| #10620649 | 2 |
| D7×#103 | 3 |
| D3×#103 | 7 |