Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C4×C7×#41 | C2 |
| prime radical | C2×C7×#41 | C22 |
| hypercenter | C4×#41 | D7 |
| hypocenter | C7 | #3504 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #90260 | C2 | semidirect |
| 4. #90230 | C2 | semidirect |
| 5. #90210 | C2 | semidirect |
| 6. #90161 | C2 | semidirect |
| 7. C2×#6433 | C2 | semidirect |
| 29. C7×#41 | Q8 | semidirect |
| 99. #41 | Dic14 | semidirect |
| 136. C7 | #3504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#41 | 2 |
| #90518 | 2 |
| #90260 | 2 |
| #90230 | 2 |
| #90210 | 2 |
| #90161 | 2 |
| C2×#6433 | 2 |
| #3504 | 7 |