Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 2. #10587893 | C2 | semidirect |
| 3. C7×#676 | C2 | semidirect |
| 4. C5×C8×D7 | C2 | semidirect |
| 5. #10587840 | C2 | semidirect |
| 6. #10587839 | C2 | semidirect |
| 7. D7×#168 | C2 | semidirect |
| 15. C5×C7×C8 | C22 | semidirect |
| 16. C7⋊#168 | C22 | semidirect |
| 17. C5×C7⋊C8 | C22 | semidirect |
| 18. C7×#168 | C22 | semidirect |
| 35. C8×D7 | D5 | semidirect |
| 42. #676 | D7 | direct (N × H) |
| 45. C5×D7 | M16 | semidirect |
| 55. C7×C8 | C2×D5 | semidirect |
| 57. C7⋊C8 | C2×D5 | semidirect |
| 66. C5×C8 | C2×D7 | semidirect |
| 68. #168 | C2×D7 | semidirect |
| 69. C5×C7 | C2×M16 | semidirect |
| 97. D7 | #676 | direct (N × H) |
| 112. C8 | D5×D7 | semidirect |
| 113. C7 | C2×#676 | semidirect |
| 114. C5 | D7×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×D7 | 2 |
| #10587893 | 2 |
| C7×#676 | 2 |
| C5×C8×D7 | 2 |
| #10587840 | 2 |
| #10587839 | 2 |
| D7×#168 | 2 |
| D7×M16 | 5 |
| C2×#676 | 7 |