Finite Group DatabasebetaFinite Group DatabasebetaOrder 1568.
470 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4×C72 | C2 | semidirect |
| 3. C2×C4×C7⋊D7 | C2 | semidirect |
| 4. C22⋊(C7⋊Dic7) | C2 | semidirect |
| 5. #11716070 | C2 | semidirect |
| 6. #11716068 | C2 | semidirect |
| 7. C4×C7⋊Dic7 | C2 | semidirect |
| 13. C22⋊(C7⋊D7) | C4 | direct (N × H) |
| 21. C22×C72 | C2×C4 | semidirect |
| 25. C2×C7⋊D7 | C2×C4 | semidirect |
| 27. C4×C72 | D4 | semidirect |
| 30. C7⋊Dic7 | C2×C4 | semidirect |
| 31. C22×C4×C7 | D7 | semidirect |
| 53. C72 | C4×D4 | semidirect |
| 57. C22×C7 | C4×D7 | semidirect |
| 63. C4×C7 | C22⋊D7 | semidirect |
| 69. C22×C4 | C7⋊D7 | semidirect |
| 89. C7 | C4×C22⋊D7 | semidirect |
| 95. C22 | C4×C7⋊D7 | semidirect |
| 101. C4 | C22⋊(C7⋊D7) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C72 | 2 |
| C2×C22⋊(C7⋊D7) | 2 |
| C2×C4×C7⋊D7 | 2 |
| C22⋊(C7⋊Dic7) | 2 |
| #11716070 | 2 |
| #11716068 | 2 |
| C4×C7⋊Dic7 | 2 |
| C4×C22⋊D7 | 7 |