Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1830 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1830 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×#376 | C2 |
| socle, prime radical | C24×C7 | C24 |
| hypercenter | C2×#376 | D7 |
| hypocenter | C7 | C2×#2645 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11730853 | C2 | direct (N × H) |
| 151. C2×C7 | #2645 | semidirect |
| 175. C7 | C2×#2645 | semidirect |
| 187. C2 | #11730853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#376 | 2 |
| C2×#89701 | 2 |
| C2×#89700 | 2 |
| #11730853 | 2 |
| C2×C7⋊#401 | 2 |
| C2×#89430 | 2 |
| C2×#2645 | 7 |