Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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 | C4×C7×C22⋊C4 | C2 |
| prime radical | C24×D7 | C22 |
| hypercenter | C4×C22⋊C4 | D7 |
| hypocenter | C7 | #2561 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#6487 | C2 | semidirect |
| 3. C4×C7×C22⋊C4 | C2 | semidirect |
| 5. #89715 | C2 | semidirect |
| 6. #89712 | C2 | semidirect |
| 7. #89446 | C2 | semidirect |
| 8. #89445 | C2 | semidirect |
| 12. C22×Dic14 | C22 | semidirect |
| 14. C2×C42×C7 | C22 | semidirect |
| 21. C2×C4⋊Dic7 | C22 | semidirect |
| 23. C2×Dic7⋊C4 | C22 | semidirect |
| 24. C7×#95 | C22 | semidirect |
| 25. C7⋊#95 | C22 | semidirect |
| 26. C7⋊#95 | C22 | semidirect |
| 62. C4×C22⋊C4 | D7 | semidirect |
| 107. C2×C42 | C2×D7 | semidirect |
| 110. #95 | C2×D7 | semidirect |
| 194. C7 | #2561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D7)⋊C4 | 2 |
| C2×#6487 | 2 |
| C4×C7×C22⋊C4 | 2 |
| #89727 | 2 |
| #89715 | 2 |
| #89712 | 2 |
| #89446 | 2 |
| #89445 | 2 |
| #2561 | 7 |