Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 147 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. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 40. C3×C4×C7 | M16 | semidirect |
| 70. C4×C7 | #208 | semidirect |
| 83. C3×C7 | #423 | semidirect |
| 98. C3×C4 | #1136 | semidirect |
| 111. C7 | #4924 | semidirect |
| 119. C4 | #66627 | semidirect |
| 123. C3 | #89696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C2×#66627 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89696 | 3 |
| #4924 | 7 |