Finite Group DatabasebetaFinite Group DatabasebetaOrder 5600.
484 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 67 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. #72243092 | C2 | semidirect |
| 3. #72243082 | C2 | semidirect |
| 4. C7×C22⋊#1044 | C2 | semidirect |
| 5. C2×#13063833 | C2 | semidirect |
| 6. #72243058 | C2 | semidirect |
| 7. C22×C7⋊#1043 | C2 | semidirect |
| 16. C5×C22⋊D35 | C4 | semidirect |
| 17. #13063794 | C4 | semidirect |
| 21. C22×C52×C7 | C2×C4 | semidirect |
| 24. C2×C7×C5⋊D5 | C2×C4 | semidirect |
| 26. C2×C5×D35 | C2×C4 | semidirect |
| 32. C7⋊#1043 | D4 | semidirect |
| 33. C5×Dic35 | C2×C4 | semidirect |
| 45. C22⋊#1044 | D7 | semidirect |
| 68. C22⋊D35 | AGL(1,𝔽5) | semidirect |
| 85. C52×C7 | C4×D4 | semidirect |
| 88. C22×C5×C7 | C2×AGL(1,𝔽5) | semidirect |
| 89. C2×D35 | C2×AGL(1,𝔽5) | semidirect |
| 110. Dic35 | C2×AGL(1,𝔽5) | semidirect |
| 119. C22×C52 | C4×D7 | semidirect |
| 122. C2×C5⋊D5 | C4×D7 | semidirect |
| 190. C5×C7 | D4×AGL(1,𝔽5) | semidirect |
| 196. C22×C7 | D5⋊AGL(1,𝔽5) | semidirect |
| 205. C52 | (C22⋊D7)⋊C4 | semidirect |
| 208. C22×C5 | D7×AGL(1,𝔽5) | semidirect |
| 269. C7 | #11717375 | semidirect |
| 271. C5 | (C22⋊D7)⋊AGL(1,𝔽5) | semidirect |
| 279. C22 | #13063833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72243092 | 2 |
| #72243084 | 2 |
| #72243082 | 2 |
| C7×C22⋊#1044 | 2 |
| C2×#13063833 | 2 |
| #72243058 | 2 |
| C22×C7⋊#1043 | 2 |
| (C22⋊D7)⋊AGL(1,𝔽5) | 5 |
| #11717375 | 7 |