Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
360 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 232 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 | C2×C4 | C24×C7 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 2. C7×#499 | C2 | direct (N × H) |
| 16. C2×#499 | C7 | direct (N × H) |
| 30. #499 | C2×C7 | direct (N × H) |
| 75. C2×C7 | #499 | direct (N × H) |
| 89. C7 | C2×#499 | direct (N × H) |
| 98. C2 | C7×#499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#125 | 2 |
| C7×#499 | 2 |
| C2×C7×#107 | 2 |
| C2×C7×#106 | 2 |
| C2×C4×C7×C8 | 2 |
| C2×#499 | 7 |