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. C3×#6548 | C2 | semidirect |
| 2. C7×#937 | C2 | semidirect |
| 3. #10621130 | C2 | semidirect |
| 4. #10620673 | C2 | semidirect |
| 5. #10620530 | C2 | semidirect |
| 7. C23×D3×C7 | C22 | semidirect |
| 16. #66636 | C22 | semidirect |
| 17. C7×#217 | C22 | semidirect |
| 20. #6548 | D3 | semidirect |
| 26. C23×C3×C7 | D4 | semidirect |
| 32. C22×C3×D7 | D4 | semidirect |
| 34. C2×C3×C4×C7 | D4 | semidirect |
| 42. C2×C3×Dic7 | D4 | semidirect |
| 62. #937 | D7 | semidirect |
| 86. C23×C7 | #67 | semidirect |
| 89. C22×D7 | #67 | semidirect |
| 93. C2×C4×C7 | #67 | semidirect |
| 100. C2×Dic7 | #67 | semidirect |
| 104. C23×D3 | C2×D7 | semidirect |
| 114. #217 | C2×D7 | semidirect |
| 147. C23×C3 | C22⋊D7 | semidirect |
| 161. C2×C3×C4 | C22⋊D7 | semidirect |
| 166. C3×C7 | B(4,𝔽2) | semidirect |
| 208. C23 | #4245 | semidirect |
| 223. C2×C4 | #4245 | semidirect |
| 224. C7 | #5244 | semidirect |
| 248. C3 | #89804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6548 | 2 |
| C7×#937 | 2 |
| #10621130 | 2 |
| #10620673 | 2 |
| #10620530 | 2 |
| #89804 | 3 |
| #5244 | 7 |