Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
296 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. C2×#1144⋊C3 | C2 | semidirect |
| 5. #6384⋊C3 | C2 | semidirect |
| 6. #89822 | C3 | semidirect |
| 20. C2×#1144 | C2×C3 | semidirect |
| 22. #6384 | C2×C3 | semidirect |
| 55. C22×ΓL(1,𝔽8) | Q16 | semidirect |
| 98. C22×C7 | C3×Q16 | semidirect |
| 118. ΓL(1,𝔽8) | #451 | semidirect |
| 156. C7 | C3×#451 | semidirect |
| 163. C22 | #1144⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×ΓL(1,𝔽8)⋊Q8 | 2 |
| ΓL(1,𝔽8)×C22⋊Q8 | 2 |
| C2×#1144⋊C3 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| #6384⋊C3 | 2 |
| #89822 | 3 |
| C3×#451 | 7 |