Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
294 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C7 |
| prime radical | C22×C7×D4 | C22 |
| 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 |
|---|---|---|
| 1. C2×C7×#125 | C2 | semidirect |
| 4. C7×#340 | C2 | semidirect |
| 5. C7×#336 | C2 | semidirect |
| 15. #2025 | C7 | direct (N × H) |
| 34. C2×#125 | C2×C7 | semidirect |
| 37. #340 | C2×C7 | semidirect |
| 38. #336 | C2×C7 | semidirect |
| 129. C7 | #2025 | 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 |
| C2×C7×#102 | 2 |
| C7×#390 | 2 |
| C7×#340 | 2 |
| C7×#336 | 2 |
| #2025 | 7 |