Finite Group DatabasebetaFinite Group DatabasebetaOrder 2240.
620 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 180 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. Q8×C7⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C7×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 4. #11765324 | C2 | semidirect |
| 5. AGL(1,𝔽5)×D28 | C2 | semidirect |
| 6. C4×D7×AGL(1,𝔽5) | C2 | semidirect |
| 7. #11765312 | C2 | semidirect |
| 10. #10587991 | C4 | semidirect |
| 12. C5×#1161 | C4 | semidirect |
| 15. #10587946 | C4 | semidirect |
| 16. #10587939 | C4 | semidirect |
| 33. C5×C7×Q8 | C2×C4 | semidirect |
| 34. D140 | C2×C4 | semidirect |
| 35. C4×D35 | C2×C4 | semidirect |
| 37. C7×Dic10 | C2×C4 | semidirect |
| 38. C5×D28 | C2×C4 | semidirect |
| 39. C4×C5×D7 | C2×C4 | semidirect |
| 40. #63306 | C2×C4 | semidirect |
| 41. #63304 | C2×C4 | semidirect |
| 43. D7×Dic5 | C2×C4 | semidirect |
| 53. Q8×AGL(1,𝔽5) | D7 | semidirect |
| 64. C7⋊AGL(1,𝔽5) | #41 | semidirect |
| 66. C7×AGL(1,𝔽5) | #41 | semidirect |
| 75. #1161 | AGL(1,𝔽5) | direct (N × H) |
| 111. C7×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 120. D28 | C2×AGL(1,𝔽5) | semidirect |
| 126. C4×D7 | C2×AGL(1,𝔽5) | semidirect |
| 134. C5×Q8 | C4×D7 | semidirect |
| 144. Dic10 | C4×D7 | semidirect |
| 145. C5×C7 | C4×#41 | semidirect |
| 174. AGL(1,𝔽5) | #1161 | direct (N × H) |
| 207. Q8 | D7×AGL(1,𝔽5) | semidirect |
| 223. C7 | #41×AGL(1,𝔽5) | semidirect |
| 224. C5 | C4×#1161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#1161 | 2 |
| Q8×C7⋊AGL(1,𝔽5) | 2 |
| C7×Q8×AGL(1,𝔽5) | 2 |
| #11765324 | 2 |
| AGL(1,𝔽5)×D28 | 2 |
| C4×D7×AGL(1,𝔽5) | 2 |
| #11765312 | 2 |
| C4×#1161 | 5 |
| #41×AGL(1,𝔽5) | 7 |