Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 236 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 |
|---|---|---|
| 4. #10620656 | C2 | semidirect |
| 5. C3×#6392 | C2 | semidirect |
| 6. #10620525 | C2 | semidirect |
| 7. #10620522 | C2 | semidirect |
| 15. C7×ΓL(1,𝔽25) | C4 | semidirect |
| 25. #6392 | D3 | semidirect |
| 39. C3×C7×C8 | C2×C4 | semidirect |
| 40. C7×C3⋊C8 | C2×C4 | semidirect |
| 83. C7×C8 | C4×D3 | semidirect |
| 95. ΓL(1,𝔽25) | Dic7 | semidirect |
| 128. C3×C8 | C2×Dic7 | semidirect |
| 129. C3⋊C8 | C2×Dic7 | semidirect |
| 130. C3×C7 | #428 | semidirect |
| 169. C8 | D3×Dic7 | semidirect |
| 170. C7 | #4881 | semidirect |
| 186. C3 | #89893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×ΓL(1,𝔽25) | 2 |
| D3×C4⋊Dic7 | 2 |
| #10620900 | 2 |
| #10620656 | 2 |
| C3×#6392 | 2 |
| #10620525 | 2 |
| #10620522 | 2 |
| #89893 | 3 |
| #4881 | 7 |