Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
282 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. #2058 | C7 | direct (N × H) |
| 29. C2×C7×C8 | Q8 | semidirect |
| 36. C7×C4⋊C4 | Q8 | semidirect |
| 101. C2×C8 | C7×Q8 | semidirect |
| 108. C4⋊C4 | C7×Q8 | semidirect |
| 139. C7 | #2058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊Q8 | 2 |
| C2×C7×#106 | 2 |
| C7×#389 | 2 |
| C7×#340 | 2 |
| C7×#336 | 2 |
| #2058 | 7 |