Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1806 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 667 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D7 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C2×C7×#384 | C2 |
| socle, prime radical | C24×C7 | C24 |
| hypercenter | C2×#384 | D7 |
| hypocenter | C7 | C2×#2843 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #11731799 | C2 | direct (N × H) |
| 34. C2×C42×C7 | Q8 | semidirect |
| 69. C42×C7 | C2×Q8 | semidirect |
| 121. C2×C42 | Dic14 | semidirect |
| 159. C42 | C2×Dic14 | semidirect |
| 160. C2×C7 | #2843 | semidirect |
| 183. C7 | C2×#2843 | semidirect |
| 195. C2 | #11731799 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#384 | 2 |
| C2×#89758 | 2 |
| C2×#89756 | 2 |
| C2×#89751 | 2 |
| C2×#89709 | 2 |
| #11731799 | 2 |
| C2×#2843 | 7 |