Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
130 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 68 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 | C22×C7 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C7 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C42×C7 ◁ C4×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. #2227 | C7 | direct (N × H) |
| 19. C7×Q16 | Q8 | semidirect |
| 66. Q16 | C7×Q8 | semidirect |
| 91. C7 | #2227 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#500 | 2 |
| C4×C7×Q16 | 2 |
| C7×#366 | 2 |
| C7×C4⋊C16 | 2 |
| C7×#358 | 2 |
| #2227 | 7 |