Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 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. #10587991 | C2 | semidirect |
| 2. #10587950 | C2 | semidirect |
| 3. C7×#688 | C2 | semidirect |
| 4. C5×#1143 | C2 | semidirect |
| 5. #10587843 | C2 | semidirect |
| 6. #10587842 | C2 | semidirect |
| 7. #10587840 | C2 | semidirect |
| 9. C5×C7×Q8 | C22 | semidirect |
| 11. D140 | C22 | semidirect |
| 17. C5×C7⋊C8 | C22 | semidirect |
| 18. C7×#168 | C22 | semidirect |
| 32. #1143 | D5 | semidirect |
| 39. #688 | D7 | semidirect |
| 49. C7×Q8 | C2×D5 | semidirect |
| 58. C7⋊C8 | C2×D5 | semidirect |
| 60. C5×Q8 | C2×D7 | semidirect |
| 69. #168 | C2×D7 | semidirect |
| 70. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 106. Q8 | D5×D7 | semidirect |
| 116. C7 | #4060 | semidirect |
| 117. C5 | #6477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587991 | 2 |
| #10587950 | 2 |
| C7×#688 | 2 |
| C5×#1143 | 2 |
| #10587843 | 2 |
| #10587842 | 2 |
| #10587840 | 2 |
| #6477 | 5 |
| #4060 | 7 |