Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 92 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. C22×C3×C7⋊C8 | C2 | semidirect |
| 3. C2×#66558 | C2 | semidirect |
| 4. #10620669 | C2 | semidirect |
| 5. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 6. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 7. #10620488 | C2 | semidirect |
| 24. C22×C7⋊C8 | D3 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 68. C22×C3×C7 | M16 | semidirect |
| 95. C7⋊C8 | #67 | semidirect |
| 126. C22×C7 | ΓL(1,𝔽25) | semidirect |
| 150. C3×C7 | #435 | semidirect |
| 171. C22×C3 | #1136 | semidirect |
| 198. C7 | #5111 | semidirect |
| 209. C22 | #66558 | semidirect |
| 217. C3 | #89783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#67 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C2×#66558 | 2 |
| #10620669 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #10620488 | 2 |
| #89783 | 3 |
| #5111 | 7 |