Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D7 |
| commutator, socle | C22×C7 | C23×C4 |
| Fitting, prime radical | C7×#525 | C2 |
| cosocle | C2×C4×C7 | C24 |
| hypercenter | #525 | D7 |
| hypocenter | C7 | #2978 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #90006 | C2 | semidirect |
| 3. #89979 | C2 | semidirect |
| 4. #89784 | C2 | semidirect |
| 5. #89783 | C2 | semidirect |
| 6. #89772 | C2 | semidirect |
| 16. C2×#1136 | C22 | semidirect |
| 17. C22×C7⋊C8 | C22 | semidirect |
| 21. C22⋊(C7⋊C8) | C22 | semidirect |
| 22. C4⋊(C7⋊C8) | C22 | semidirect |
| 23. #6377 | C22 | semidirect |
| 24. C4×C7⋊C8 | C22 | semidirect |
| 159. C7 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#525 | 2 |
| #90006 | 2 |
| #89979 | 2 |
| #89784 | 2 |
| #89783 | 2 |
| #89772 | 2 |
| #2978 | 7 |