Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24909135 | C2 | semidirect |
| 3. #24909134 | C2 | semidirect |
| 4. #24909114 | C2 | semidirect |
| 5. #24907507 | C2 | semidirect |
| 6. #24907266 | C2 | semidirect |
| 7. C83×#2122 | C2 | semidirect |
| 8. C22×#13050575 | C4 | semidirect |
| 16. #19127737 | C4 | semidirect |
| 17. #19127706 | C4 | semidirect |
| 18. #19127705 | C4 | semidirect |
| 224. #2122 | D83 | semidirect |
| 227. C83 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917108 | 2 |
| #24909135 | 2 |
| #24909134 | 2 |
| #24909114 | 2 |
| #24907507 | 2 |
| #24907266 | 2 |
| C83×#2122 | 2 |
| #13231 | 83 |