Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
146 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 29 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 |
|---|---|---|
| 4. C22×#1144 | C3 | semidirect |
| 34. #1144 | A4 | semidirect |
| 40. C22⋊ΓL(1,𝔽8) | Q16 | semidirect |
| 76. C22×C7 | C3×Q16 | semidirect |
| 128. C7 | A4×Q16 | semidirect |
| 132. C22 | #1144⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊ΓL(1,𝔽8) | 2 |
| Dic14⋊A4 | 2 |
| (C7⋊C8)⋊A4 | 2 |
| C22×#1144 | 3 |
| #1144⋊C3 | 4 |
| A4×Q16 | 7 |