Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 112 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×#1136⋊C3 | C2 | semidirect |
| 3. #6407⋊C3 | C2 | direct (N × H) |
| 4. C2×#6407 | C3 | semidirect |
| 12. #1136⋊C3 | C22 | semidirect |
| 15. C2×#1136 | C2×C3 | semidirect |
| 16. #6407 | C2×C3 | semidirect |
| 37. #1136 | C22×C3 | semidirect |
| 77. C2×ΓL(1,𝔽8) | #100 | semidirect |
| 104. ΓL(1,𝔽8) | C2×#100 | semidirect |
| 117. C2×C7 | C3×#100 | semidirect |
| 141. C7 | C2×C3×#100 | semidirect |
| 161. C2 | #6407⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×ΓL(1,𝔽8) | 2 |
| C2×#1136⋊C3 | 2 |
| #6407⋊C3 | 2 |
| C2×#6407 | 3 |
| C2×C3×#100 | 7 |