Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 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 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2845 | C2 |
| prime radical | C23×D7 | C24 |
| hypercenter | #2845 | D7 |
| hypocenter | C7 | C2×#2845 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2845 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2845 | C2 | semidirect |
| 3. #11735389 | C2 | semidirect |
| 5. #11731664 | C2 | semidirect |
| 46. #2845 | D7 | direct (N × H) |
| 157. D7 | #2845 | direct (N × H) |
| 176. C7 | C2×#2845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2845 | 2 |
| D7×#398 | 2 |
| #11735389 | 2 |
| D7×#382 | 2 |
| #11731664 | 2 |
| C2×#2845 | 7 |