Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 64 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×#1004 | C2 | semidirect |
| 2. #10621420 | C2 | semidirect |
| 3. #10621135 | C2 | semidirect |
| 4. C3×#6408 | C2 | semidirect |
| 5. #10620531 | C2 | semidirect |
| 7. C23×D21 | C22 | semidirect |
| 16. #66636 | C22 | semidirect |
| 18. C3×C22⋊Dic7 | C22 | semidirect |
| 24. #6408 | D3 | semidirect |
| 26. C23×C3×C7 | D4 | semidirect |
| 32. C22×D3×C7 | D4 | semidirect |
| 34. C2×C3×C4×C7 | D4 | semidirect |
| 41. C2×C7×Dic3 | D4 | semidirect |
| 57. C22⋊Dic7 | C2×D3 | semidirect |
| 60. #1004 | D7 | semidirect |
| 85. C23×C7 | D12 | semidirect |
| 99. C2×C4×C7 | D12 | semidirect |
| 145. C23×C3 | C22⋊D7 | semidirect |
| 151. C22×D3 | C22⋊D7 | semidirect |
| 154. C2×C3×C4 | C22⋊D7 | semidirect |
| 161. C2×Dic3 | C22⋊D7 | semidirect |
| 166. C3×C7 | B(4,𝔽2) | semidirect |
| 208. C23 | #4247 | semidirect |
| 223. C2×C4 | #4247 | semidirect |
| 224. C7 | #4741 | semidirect |
| 248. C3 | #90016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1004 | 2 |
| #10621420 | 2 |
| #10621135 | 2 |
| C3×#6408 | 2 |
| #10620531 | 2 |
| #90016 | 3 |
| #4741 | 7 |