Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×C7×M16 | C2 | semidirect |
| 3. C5×#1136 | C2 | semidirect |
| 4. C5×#1131 | C2 | semidirect |
| 5. C5×C8×D7 | C2 | semidirect |
| 13. C5×C7×C8 | C22 | semidirect |
| 14. C5×C7⋊C8 | C22 | semidirect |
| 15. D7×M16 | C5 | direct (N × H) |
| 26. C7×M16 | C2×C5 | semidirect |
| 27. #1136 | C2×C5 | semidirect |
| 28. #1131 | C2×C5 | semidirect |
| 29. C8×D7 | C2×C5 | semidirect |
| 33. C5×M16 | D7 | direct (N × H) |
| 38. C5×D7 | M16 | direct (N × H) |
| 46. C7×C8 | C22×C5 | semidirect |
| 47. C7⋊C8 | C22×C5 | semidirect |
| 56. C5×C8 | C2×D7 | semidirect |
| 57. C5×C7 | C2×M16 | semidirect |
| 78. M16 | C5×D7 | direct (N × H) |
| 83. D7 | C5×M16 | direct (N × H) |
| 96. C8 | C2×C5×D7 | semidirect |
| 97. C7 | C2×C5×M16 | semidirect |
| 98. C5 | D7×M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D7 | 2 |
| C5×C7×M16 | 2 |
| C5×#1136 | 2 |
| C5×#1131 | 2 |
| C5×C8×D7 | 2 |
| D7×M16 | 5 |
| C2×C5×M16 | 7 |