Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1630 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 283 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. #24910117 | C2 | semidirect |
| 3. #24907871 | C2 | semidirect |
| 4. #24907744 | C2 | semidirect |
| 5. #24907411 | C2 | semidirect |
| 6. C4×#14581707 | C2 | semidirect |
| 7. C4×H(5,𝔽2)×C83 | C2 | semidirect |
| 9. C22×(C2×D83)⋊C4 | C22 | semidirect |
| 10. #19127888 | C4 | semidirect |
| 18. #19127573 | C22 | semidirect |
| 19. #19127556 | C22 | semidirect |
| 20. C4×C22⋊Dic83 | C22 | semidirect |
| 21. #19127468 | C22 | semidirect |
| 33. #14581760 | C2×C4 | semidirect |
| 45. #14581707 | C2×C4 | semidirect |
| 55. C23×C4×C83 | D4 | semidirect |
| 69. C2×C4⋊C4×C83 | D4 | semidirect |
| 72. C2×C22⋊C4×C83 | D4 | semidirect |
| 75. C2×C42×C83 | D4 | semidirect |
| 80. C23×D83 | C22×C4 | semidirect |
| 92. C22⋊Dic83 | C22×C4 | semidirect |
| 222. C4×H(5,𝔽2) | D83 | semidirect |
| 229. C83 | #21482 | semidirect |
| 260. C23×C4 | C22⋊D83 | semidirect |
| 277. C2×C4⋊C4 | C22⋊D83 | semidirect |
| 288. C2×C22⋊C4 | C22⋊D83 | semidirect |
| 292. C2×C42 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127888 | 2 |
| #24910117 | 2 |
| #24907871 | 2 |
| #24907744 | 2 |
| #24907411 | 2 |
| C4×#14581707 | 2 |
| C4×H(5,𝔽2)×C83 | 2 |
| #21482 | 83 |