Finite Group DatabasebetaFinite Group DatabasebetaOrder 2240.
572 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 106 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. C23×C7×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×C22⋊(C7⋊AGL(1,𝔽5)) | C2 | semidirect |
| 4. C2×(C2×D7)⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊Dic7 | C2 | semidirect |
| 12. C2×C22⋊D35 | C4 | semidirect |
| 13. C2×C5×C22⋊D7 | C4 | semidirect |
| 16. C2×#63307 | C4 | semidirect |
| 17. C2×#63305 | C4 | semidirect |
| 24. C22×D35 | C2×C4 | semidirect |
| 31. C22×C5×D7 | C2×C4 | semidirect |
| 42. C2×C7×AGL(1,𝔽5) | D4 | semidirect |
| 44. C2×Dic35 | C2×C4 | semidirect |
| 46. C2×C5×Dic7 | C2×C4 | semidirect |
| 56. C23×AGL(1,𝔽5) | D7 | semidirect |
| 62. C22×C5×C7 | C22⋊C4 | semidirect |
| 70. C2×C7×D5 | C22⋊C4 | semidirect |
| 94. C2×C22⋊D7 | AGL(1,𝔽5) | semidirect |
| 136. C22×D7 | C2×AGL(1,𝔽5) | semidirect |
| 151. C2×Dic7 | C2×AGL(1,𝔽5) | semidirect |
| 171. C2×AGL(1,𝔽5) | C22⋊D7 | semidirect |
| 180. C5×C7 | #386 | semidirect |
| 196. C22×C7 | C22⋊AGL(1,𝔽5) | semidirect |
| 212. C22×C5 | (C2×D7)⋊C4 | semidirect |
| 223. C2×D5 | (C2×D7)⋊C4 | semidirect |
| 293. C7 | #65779 | semidirect |
| 294. C5 | #89985 | semidirect |
| 312. C22 | (C2×D7)⋊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×D5×C22⋊D7 | 2 |
| C2×C22⋊(C7⋊AGL(1,𝔽5)) | 2 |
| C2×(C2×D7)⋊AGL(1,𝔽5) | 2 |
| (C2×AGL(1,𝔽5))⋊Dic7 | 2 |
| #89985 | 5 |
| #65779 | 7 |