Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 2. C7×#924 | C2 | semidirect |
| 3. C22×C3×C7⋊C8 | C2 | semidirect |
| 4. C2×#66568 | C2 | semidirect |
| 5. #10620520 | C2 | semidirect |
| 6. #10620508 | C2 | semidirect |
| 7. #10620504 | C2 | semidirect |
| 25. C22×C7⋊C8 | D3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 61. #924 | D7 | semidirect |
| 68. C22×C3×C7 | SD16 | semidirect |
| 95. C7⋊C8 | #67 | semidirect |
| 123. C22×C7 | #204 | semidirect |
| 150. C3×C7 | #465 | semidirect |
| 171. C22×C3 | #1143 | semidirect |
| 198. C7 | #5114 | semidirect |
| 209. C22 | #66568 | semidirect |
| 217. C3 | #89820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621413 | 2 |
| C7×#924 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C2×#66568 | 2 |
| #10620520 | 2 |
| #10620508 | 2 |
| #10620504 | 2 |
| #89820 | 3 |
| #5114 | 7 |