Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
356 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D21 |
| commutator | C2×C3×C7 | C2×C42 |
| Fitting | C3×C7×#95 | C2 |
| socle, prime radical, cosocle | C23×C3×C7 | C23 |
| hypercenter | #95 | D21 |
| hypocenter | C3×C7 | #376 |
| LCS | G ▷ C2×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C4×Dic21 | C4 | semidirect |
| 64. C3×C7 | #376 | semidirect |
| 85. C7 | #4648 | semidirect |
| 95. C3 | #89420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic21 | 2 |
| C3×C7×#95 | 2 |
| #10620670 | 2 |
| #89420 | 3 |
| #4648 | 7 |