Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 62 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. C2×#63304 | C2 | semidirect |
| 3. C2×D5×Dic7 | C2 | semidirect |
| 4. #10587902 | C2 | semidirect |
| 5. C7×#685 | C2 | semidirect |
| 6. C4×C5×Dic7 | C2 | semidirect |
| 7. Dic7⋊Dic5 | C2 | semidirect |
| 15. #63307 | C4 | semidirect |
| 23. C2×D35 | C2×C4 | semidirect |
| 26. C2×C7×D5 | C2×C4 | semidirect |
| 29. C5×Dic7 | C2×C4 | semidirect |
| 30. C5×Dic7 | D4 | semidirect |
| 38. C4×Dic7 | D5 | semidirect |
| 44. #685 | D7 | semidirect |
| 71. C5×C7 | C4×D4 | semidirect |
| 83. Dic7 | C4×D5 | semidirect |
| 84. Dic7 | D20 | semidirect |
| 91. C2×D5 | C4×D7 | semidirect |
| 124. C7 | C4×D20 | semidirect |
| 125. C5 | (C22⋊D7)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63307 | 2 |
| C2×#63304 | 2 |
| C2×D5×Dic7 | 2 |
| #10587902 | 2 |
| C7×#685 | 2 |
| C4×C5×Dic7 | 2 |
| Dic7⋊Dic5 | 2 |
| (C22⋊D7)⋊C4 | 5 |
| C4×D20 | 7 |