Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1380 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 195 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×D664 | C2 | semidirect |
| 2. C2×#19128139 | C2 | semidirect |
| 3. #24917044 | C2 | semidirect |
| 4. #24909394 | C2 | semidirect |
| 5. #24909377 | C2 | semidirect |
| 6. #24909180 | C2 | semidirect |
| 7. C83×#2112 | C2 | semidirect |
| 9. C2×#14581814 | C22 | semidirect |
| 17. C2×#14581737 | C22 | semidirect |
| 18. C2×D1328 | C22 | semidirect |
| 19. #19127942 | C22 | semidirect |
| 20. #19127937 | C22 | semidirect |
| 22. #19127739 | C22 | semidirect |
| 24. #19127503 | C22 | semidirect |
| 26. C2×M32×C83 | C22 | semidirect |
| 27. C22⋊C16×C83 | C22 | semidirect |
| 37. C2×Dic332 | C23 | semidirect |
| 45. C2×D664 | D4 | semidirect |
| 47. C2×D664 | C23 | semidirect |
| 56. #14581726 | C23 | semidirect |
| 67. C2×C16×C83 | C23 | semidirect |
| 158. C22×C83 | #509 | semidirect |
| 185. #2112 | D83 | semidirect |
| 186. C83 | #33517 | semidirect |
| 199. C2×M32 | C2×D83 | semidirect |
| 206. C22⋊C16 | C2×D83 | semidirect |
| 242. C2×C16 | C22×D83 | semidirect |
| 343. C22 | #19128139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D664 | 2 |
| C2×#19128139 | 2 |
| #24917044 | 2 |
| #24909394 | 2 |
| #24909377 | 2 |
| #24909180 | 2 |
| C83×#2112 | 2 |
| #33517 | 83 |