Finite Group DatabasebetaFinite Group DatabasebetaOrder 2240.
468 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×Dic7⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊Dic7 | C2 | semidirect |
| 15. C22⋊Dic35 | C4 | semidirect |
| 16. C5×C22⋊Dic7 | C4 | semidirect |
| 17. #10587855 | C4 | semidirect |
| 35. C2×Dic35 | C2×C4 | semidirect |
| 36. C2×C5×Dic7 | C2×C4 | semidirect |
| 50. C22×C5×C7 | C4⋊C4 | semidirect |
| 56. C2×C7×D5 | C4⋊C4 | semidirect |
| 76. C22⋊Dic7 | AGL(1,𝔽5) | semidirect |
| 116. C2×Dic7 | C2×AGL(1,𝔽5) | semidirect |
| 136. C5×C7 | #385 | semidirect |
| 152. C22×C7 | C4⋊AGL(1,𝔽5) | semidirect |
| 160. C22×C5 | Dic7⋊C4 | semidirect |
| 166. C2×D5 | Dic7⋊C4 | semidirect |
| 221. C7 | #65699 | semidirect |
| 222. C5 | #89718 | semidirect |
| 233. C22 | Dic7⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7⋊AGL(1,𝔽5) | 2 |
| C2×C7×C22⋊AGL(1,𝔽5) | 2 |
| C2×Dic7⋊AGL(1,𝔽5) | 2 |
| D5×C22⋊Dic7 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic7 | 2 |
| #89718 | 5 |
| #65699 | 7 |