Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 77 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×C22⋊Q8 | C2 | semidirect |
| 2. C2×#66634 | C2 | semidirect |
| 4. C22×C3⋊(C7⋊C8) | C2 | semidirect |
| 5. #10620674 | C2 | semidirect |
| 6. #10620648 | C2 | semidirect |
| 7. #10620647 | C2 | semidirect |
| 22. C7×C22⋊Q8 | D3 | semidirect |
| 45. C3⋊(C7⋊C8) | D4 | semidirect |
| 59. C3×C22⋊Q8 | D7 | semidirect |
| 68. C22×C3×C7 | SD16 | semidirect |
| 116. C22⋊Q8 | D21 | semidirect |
| 123. C22×C7 | #215 | semidirect |
| 150. C3×C7 | #465 | semidirect |
| 171. C22×C3 | #1143 | semidirect |
| 198. C7 | #5048 | semidirect |
| 209. C22 | #66634 | semidirect |
| 217. C3 | #89820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C22⋊Q8 | 2 |
| C2×#66634 | 2 |
| #10621413 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| #10620674 | 2 |
| #10620648 | 2 |
| #10620647 | 2 |
| #89820 | 3 |
| #5048 | 7 |