Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
184 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C5×C7×C4⋊C4 | C2 | semidirect |
| 4. C5×C4⋊Dic7 | C2 | semidirect |
| 5. C5×Dic7⋊C4 | C2 | semidirect |
| 12. C4×C5×D7 | C4 | semidirect |
| 13. D7×C4⋊C4 | C5 | direct (N × H) |
| 20. C4×C5×C7 | C2×C4 | semidirect |
| 22. C5×Dic7 | C2×C4 | semidirect |
| 25. C7×C4⋊C4 | C2×C5 | semidirect |
| 26. C4⋊Dic7 | C2×C5 | semidirect |
| 27. Dic7⋊C4 | C2×C5 | semidirect |
| 32. C5×C4⋊C4 | D7 | direct (N × H) |
| 36. C5×D7 | C4⋊C4 | direct (N × H) |
| 43. C4×D7 | C4×C5 | semidirect |
| 51. C5×C7 | C2×C4⋊C4 | semidirect |
| 58. C4×C7 | C2×C4×C5 | semidirect |
| 60. Dic7 | C2×C4×C5 | semidirect |
| 68. C4×C5 | C4×D7 | semidirect |
| 73. C4⋊C4 | C5×D7 | direct (N × H) |
| 77. D7 | C5×C4⋊C4 | direct (N × H) |
| 89. C7 | C2×C5×C4⋊C4 | semidirect |
| 90. C5 | D7×C4⋊C4 | direct (N × H) |
| 98. C4 | C4×C5×D7 | semidirect |
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×C4⋊C4 | 2 |
| C5×C4⋊Dic7 | 2 |
| C5×Dic7⋊C4 | 2 |
| D7×C4⋊C4 | 5 |
| C2×C5×C4⋊C4 | 7 |