Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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. C5×#1161 | C2 | semidirect |
| 2. D7×D20 | C2 | semidirect |
| 3. #10587905 | C2 | semidirect |
| 4. C7×#688 | C2 | semidirect |
| 5. #10587842 | C2 | semidirect |
| 6. #10587841 | C2 | semidirect |
| 7. #10587838 | C2 | semidirect |
| 9. C5×C7×Q8 | C22 | semidirect |
| 13. C5×D28 | C22 | semidirect |
| 17. C7⋊#168 | C22 | semidirect |
| 18. C7×#168 | C22 | semidirect |
| 29. #1161 | D5 | semidirect |
| 39. #688 | D7 | semidirect |
| 49. C7×Q8 | C2×D5 | semidirect |
| 54. D28 | 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 | #4095 | semidirect |
| 117. C5 | #6477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1161 | 2 |
| D7×D20 | 2 |
| #10587905 | 2 |
| C7×#688 | 2 |
| #10587842 | 2 |
| #10587841 | 2 |
| #10587838 | 2 |
| #6477 | 5 |
| #4095 | 7 |