Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
224 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C2×D4 |
| commutator | C2×C4 | C22×C4×C7 |
| Frattini, cosocle | C22×C4 | C23×C7 |
| socle | C22×C7 | C4×D4 |
| prime radical | C2×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C22×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#108 | C2 | semidirect |
| 5. C7×#405 | C2 | semidirect |
| 6. C7×#339 | C2 | semidirect |
| 7. C7×#336 | C2 | semidirect |
| 17. C7×#103 | C4 | semidirect |
| 18. C7×#103 | C4 | semidirect |
| 19. C7×#102 | C4 | semidirect |
| 20. C7×#102 | C4 | semidirect |
| 25. #1929 | C7 | direct (N × H) |
| 56. C2×#108 | C2×C7 | semidirect |
| 60. #405 | C2×C7 | semidirect |
| 61. #339 | C2×C7 | semidirect |
| 62. #336 | C2×C7 | semidirect |
| 100. #103 | C4×C7 | semidirect |
| 101. #103 | C4×C7 | semidirect |
| 102. #102 | C4×C7 | semidirect |
| 103. #102 | C4×C7 | semidirect |
| 188. C7 | #1929 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#108 | 2 |
| C2×C7×#104 | 2 |
| C7×#416 | 2 |
| C7×#408 | 2 |
| C7×#405 | 2 |
| C7×#339 | 2 |
| C7×#336 | 2 |
| #1929 | 7 |