Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D7 |
| commutator, cosocle | C2×C4×C7 | C24 |
| Frattini | C2×C4 | C23×D7 |
| Fitting | C7×#460 | C2 |
| socle | C22×C7 | C22×D4 |
| hypercenter | #460 | D7 |
| hypocenter | C7 | #3287 |
| LCS | G ▷ C2×C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #460 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6479 | C2 | semidirect |
| 2. #90409 | C2 | semidirect |
| 3. #90268 | C2 | semidirect |
| 4. C7×#460 | C2 | semidirect |
| 5. #89944 | C2 | semidirect |
| 6. #89845 | C2 | semidirect |
| 7. C4×#1144 | C2 | semidirect |
| 8. #89620 | C2 | semidirect |
| 9. #89606 | C2 | semidirect |
| 10. #89553 | C2 | semidirect |
| 11. #89547 | C2 | semidirect |
| 70. #1144 | D4 | semidirect |
| 89. #460 | D7 | semidirect |
| 172. C4×C7 | #135 | semidirect |
| 259. C7 | #3287 | semidirect |
| 276. C4 | #6479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6479 | 2 |
| #90409 | 2 |
| #90268 | 2 |
| C7×#460 | 2 |
| #89944 | 2 |
| #89845 | 2 |
| C4×#1144 | 2 |
| #89620 | 2 |
| #89606 | 2 |
| #89553 | 2 |
| #89547 | 2 |
| #3287 | 7 |