Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 96 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. C2×#66558 | C2 | semidirect |
| 3. C2×D3×C7⋊C8 | C2 | semidirect |
| 4. #10620669 | C2 | semidirect |
| 5. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 6. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 30. C22⋊(C7⋊C8) | D3 | semidirect |
| 176. C3×C7 | #408 | semidirect |
| 234. C7 | #4727 | semidirect |
| 256. C3 | #90006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C2×#66558 | 2 |
| C2×D3×C7⋊C8 | 2 |
| #10620669 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #90006 | 3 |
| #4727 | 7 |