Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
688 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24909134 | C2 | semidirect |
| 3. #24909112 | C2 | semidirect |
| 4. #24907433 | C2 | semidirect |
| 5. #24905591 | C2 | semidirect |
| 6. #24905583 | C2 | semidirect |
| 7. C83×#2883 | C2 | semidirect |
| 8. C2×#14581817 | C4 | semidirect |
| 9. C22×#13050575 | C4 | semidirect |
| 17. #19127706 | C4 | semidirect |
| 18. #19127697 | C4 | semidirect |
| 31. C22×D332 | C2×C4 | semidirect |
| 39. C2×#13050574 | C2×C4 | semidirect |
| 40. C22×C83⋊C8 | C2×C4 | semidirect |
| 48. #14581751 | C2×C4 | semidirect |
| 260. #2883 | D83 | semidirect |
| 266. C83 | #13102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916731 | 2 |
| #24909134 | 2 |
| #24909112 | 2 |
| #24907433 | 2 |
| #24905591 | 2 |
| #24905583 | 2 |
| C83×#2883 | 2 |
| #13102 | 83 |