Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
504 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D7 |
| commutator, socle, prime radical, cosocle | C23×C7 | C24 |
| Frattini | C23 | C23×D7 |
| Fitting | C2×C4×C7×Q8 | C2 |
| hypercenter | C2×C4×Q8 | D7 |
| hypocenter | C7 | #2399 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 49. C4×Dic7 | Q8 | semidirect |
| 158. C7 | #2399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×Q8 | 2 |
| C2×C4×Dic14 | 2 |
| #90001 | 2 |
| #89755 | 2 |
| #89752 | 2 |
| #89751 | 2 |
| #89704 | 2 |
| C4×Dic7⋊C4 | 2 |
| #2399 | 7 |