Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 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. C2×#19128137 | C2 | semidirect |
| 2. #24917044 | C2 | semidirect |
| 3. #24909392 | C2 | semidirect |
| 4. #24909375 | C2 | semidirect |
| 5. #24909179 | C2 | semidirect |
| 6. #24909074 | C2 | semidirect |
| 7. C23×D8×C83 | C2 | semidirect |
| 8. C2×#14581814 | C22 | semidirect |
| 11. C2×#14581736 | C22 | semidirect |
| 12. C2×#14581733 | C22 | semidirect |
| 13. C2×#14581732 | C22 | semidirect |
| 14. #19127942 | C22 | semidirect |
| 15. #19127937 | C22 | semidirect |
| 17. #19127739 | C22 | semidirect |
| 19. #19127502 | C22 | semidirect |
| 20. C22⋊(C83⋊C16) | C22 | semidirect |
| 30. C2×Dic332 | C23 | semidirect |
| 32. C2×D664 | C23 | semidirect |
| 42. C2×C83⋊C16 | C23 | semidirect |
| 43. #14581726 | C23 | semidirect |
| 61. C2×D8×C83 | D4 | semidirect |
| 162. C22×C83 | #509 | semidirect |
| 179. C23×D8 | D83 | semidirect |
| 186. C83 | #33517 | semidirect |
| 226. C2×D8 | C22⋊D83 | semidirect |
| 343. C22 | #19128137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128137 | 2 |
| #24917044 | 2 |
| #24909392 | 2 |
| #24909375 | 2 |
| #24909179 | 2 |
| #24909074 | 2 |
| C23×D8×C83 | 2 |
| #33517 | 83 |