Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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, socle, cosocle | C23×C7 | C24 |
| Fitting | C7×#379 | C2 |
| prime radical | C25×C7 | C22 |
| hypercenter | #379 | D7 |
| hypocenter | C7 | #2483 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #89725 | C2 | semidirect |
| 4. #89722 | C2 | semidirect |
| 5. #89715 | C2 | semidirect |
| 14. C2×C4⋊Dic7 | C22 | semidirect |
| 15. C7⋊#95 | C22 | semidirect |
| 16. C7⋊#95 | C22 | semidirect |
| 125. C7 | #2483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic7 | 2 |
| C7×#379 | 2 |
| #89725 | 2 |
| #89722 | 2 |
| #89715 | 2 |
| #2483 | 7 |