Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
644 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 208 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. C22×Dic42 | C2 | semidirect |
| 3. C2×C7×C4⋊Dic3 | C2 | semidirect |
| 4. C2×Dic3⋊Dic7 | C2 | semidirect |
| 6. #10620922 | C2 | direct (N × H) |
| 12. C2×Dic42 | C22 | semidirect |
| 17. C7×C4⋊Dic3 | C22 | semidirect |
| 18. Dic3⋊Dic7 | C22 | semidirect |
| 30. C22×C3×D7 | Q8 | semidirect |
| 57. C2×C4⋊Dic3 | D7 | semidirect |
| 67. C2×C3×D7 | C2×Q8 | semidirect |
| 76. C22×D7 | Dic6 | semidirect |
| 98. C4⋊Dic3 | C2×D7 | semidirect |
| 100. C2×C3×C7 | C22⋊Q8 | semidirect |
| 118. C2×D7 | C2×Dic6 | semidirect |
| 138. C3×C7 | C2×C22⋊Q8 | semidirect |
| 151. C2×C7 | #924 | semidirect |
| 183. C7 | C2×#924 | semidirect |
| 185. C2×C3 | #6460 | semidirect |
| 201. C3 | C2×#6460 | semidirect |
| 203. C2 | #10620922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C22×C3×C4×D7 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×Dic3⋊Dic7 | 2 |
| C2×(C2×D7)⋊Dic3 | 2 |
| #10620922 | 2 |
| C2×#6460 | 3 |
| C2×#924 | 7 |