Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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. Q8×D35 | C2 | semidirect |
| 3. C5×C7×SD16 | C2 | semidirect |
| 4. #10587905 | C2 | semidirect |
| 5. #10587904 | C2 | semidirect |
| 6. #10587894 | C2 | semidirect |
| 7. C8×D35 | C2 | semidirect |
| 9. C5×C7×Q8 | C22 | semidirect |
| 16. Dic70 | C22 | semidirect |
| 17. C5×C7×C8 | C22 | semidirect |
| 18. C7⋊#168 | C22 | semidirect |
| 31. C7×SD16 | D5 | semidirect |
| 38. C5×SD16 | D7 | semidirect |
| 46. D35 | SD16 | direct (N × H) |
| 48. C7×Q8 | C2×D5 | semidirect |
| 56. C7×C8 | C2×D5 | semidirect |
| 59. C5×Q8 | C2×D7 | semidirect |
| 67. C5×C8 | C2×D7 | semidirect |
| 69. C5×C7 | C2×SD16 | semidirect |
| 92. SD16 | D35 | direct (N × H) |
| 105. Q8 | C2×D35 | semidirect |
| 112. C8 | C2×D35 | semidirect |
| 113. C7 | D5×SD16 | semidirect |
| 114. C5 | D7×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D35 | 2 |
| D4×D35 | 2 |
| C5×C7×SD16 | 2 |
| #10587905 | 2 |
| #10587904 | 2 |
| #10587894 | 2 |
| C8×D35 | 2 |
| D7×SD16 | 5 |
| D5×SD16 | 7 |