Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
100 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 33 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. C4⋊(C7⋊AGL(1,𝔽5)) | C2 | semidirect |
| 3. D5⋊(C7⋊C8) | C2 | semidirect |
| 6. C5×C7×D4 | C4 | semidirect |
| 8. C7×D20 | C4 | semidirect |
| 35. C7×D4 | AGL(1,𝔽5) | semidirect |
| 41. C5×D4 | Dic7 | semidirect |
| 43. D20 | Dic7 | semidirect |
| 46. C5×C7 | #102 | semidirect |
| 80. D4 | C7⋊AGL(1,𝔽5) | semidirect |
| 84. C7 | #4007 | semidirect |
| 85. C5 | #6406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×D5 | 2 |
| C4⋊(C7⋊AGL(1,𝔽5)) | 2 |
| D5⋊(C7⋊C8) | 2 |
| #6406 | 5 |
| #4007 | 7 |