Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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 | C23×D7 |
| commutator | C22×C7 | C23×C4 |
| Fitting | C7×#390 | C2 |
| socle, cosocle | C23×C7 | C24 |
| prime radical | C22×#1159 | C2 |
| hypercenter | #390 | D7 |
| hypocenter | C7 | #2311 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D7×C4⋊C4 | C2 | semidirect |
| 3. C2×#6435 | C2 | semidirect |
| 4. C7×#390 | C2 | semidirect |
| 5. #89993 | C2 | semidirect |
| 6. #89746 | C2 | semidirect |
| 7. #89728 | C2 | semidirect |
| 8. #89714 | C2 | semidirect |
| 9. #89701 | C2 | semidirect |
| 15. C2×#1159 | C4 | semidirect |
| 37. C2×C7×D4 | C2×C4 | semidirect |
| 46. C22×Dic7 | C2×C4 | semidirect |
| 59. C2×Dic14 | C2×C4 | semidirect |
| 75. #390 | D7 | semidirect |
| 112. C4×D7 | C22⋊C4 | semidirect |
| 169. C2×D4 | C4×D7 | semidirect |
| 237. C7 | #2311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1159 | 2 |
| C2×D7×C4⋊C4 | 2 |
| C2×#6435 | 2 |
| C7×#390 | 2 |
| #89993 | 2 |
| #89746 | 2 |
| #89728 | 2 |
| #89714 | 2 |
| #89701 | 2 |
| #2311 | 7 |