Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 | C2×C7 | C22×C42 |
| Fitting | C7×#376 | C2 |
| socle, cosocle | C23×C7 | C24 |
| prime radical | C22×D28 | C22 |
| hypercenter | #376 | D7 |
| hypocenter | C7 | #2275 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#376 | C2 | semidirect |
| 3. C4×C4⋊Dic7 | C2 | semidirect |
| 4. #89438 | C2 | semidirect |
| 5. D7×#95 | C2 | semidirect |
| 12. C4×D28 | C4 | semidirect |
| 24. C2×C4×D7 | C2×C4 | semidirect |
| 25. C42×C7 | C2×C4 | semidirect |
| 26. (C2×D7)⋊C4 | C2×C4 | semidirect |
| 27. C4⋊Dic7 | C2×C4 | semidirect |
| 32. #376 | D7 | semidirect |
| 46. D28 | C42 | semidirect |
| 79. C42 | C4×D7 | semidirect |
| 98. C7 | #2275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D28 | 2 |
| C7×#376 | 2 |
| C4×C4⋊Dic7 | 2 |
| #89438 | 2 |
| D7×#95 | 2 |
| #2275 | 7 |