Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
496 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 214 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×C7×2−1+4 | C2 | semidirect |
| 2. C7×#1010 | C2 | semidirect |
| 3. C7×#951 | C2 | semidirect |
| 4. C7×#950 | C2 | semidirect |
| 5. C7×#948 | C2 | semidirect |
| 6. C2×C7×#216 | C2 | semidirect |
| 7. C7×#942 | C2 | semidirect |
| 26. C7×2−1+4 | D3 | semidirect |
| 32. #5838 | C7 | direct (N × H) |
| 66. C3×2−1+4 | C2×C7 | semidirect |
| 67. #1010 | C2×C7 | semidirect |
| 68. #951 | C2×C7 | semidirect |
| 69. #950 | C2×C7 | semidirect |
| 70. #948 | C2×C7 | semidirect |
| 71. C2×#216 | C2×C7 | semidirect |
| 72. #942 | C2×C7 | semidirect |
| 119. 2−1+4 | D3×C7 | semidirect |
| 149. C3×C7 | #578 | semidirect |
| 194. C7 | #5838 | direct (N × H) |
| 206. C3 | C7×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×2−1+4 | 2 |
| C7×#1010 | 2 |
| C7×#951 | 2 |
| C7×#950 | 2 |
| C7×#948 | 2 |
| C2×C7×#216 | 2 |
| C7×#942 | 2 |
| C7×#578 | 3 |
| #5838 | 7 |