Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
256 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 136 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 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C7 |
| Frattini, cosocle | C42 | C23×C7 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C7×#333 | C2 | direct (N × H) |
| 13. C2×#333 | C7 | direct (N × H) |
| 29. #333 | C2×C7 | direct (N × H) |
| 74. C2×C7 | #333 | direct (N × H) |
| 90. C7 | C2×#333 | direct (N × H) |
| 100. C2 | C7×#333 | 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×C4⋊C8 | 2 |
| C7×#333 | 2 |
| C2×#333 | 7 |