Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 6. #89953 | C3 | semidirect |
| 51. ΓL(1,𝔽8)⋊C4 | Q16 | semidirect |
| 84. Dic7 | C3×Q16 | semidirect |
| 95. ΓL(1,𝔽8) | #494 | semidirect |
| 123. C7 | C3×#494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×ΓL(1,𝔽8) | 2 |
| #6507⋊C3 | 2 |
| C2×#1144⋊C3 | 2 |
| C2×Dic28⋊C3 | 2 |
| C8×ΓL(1,𝔽8)⋊C4 | 2 |
| #89953 | 3 |
| C3×#494 | 7 |