Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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×#19127739 | C2 | semidirect |
| 2. #24909668 | C2 | semidirect |
| 3. #24909651 | C2 | semidirect |
| 4. #24909252 | C2 | semidirect |
| 5. #24909175 | C2 | semidirect |
| 6. #24909074 | C2 | semidirect |
| 14. #19127528 | C22 | semidirect |
| 15. #19127526 | C22 | semidirect |
| 16. #19127505 | C22 | semidirect |
| 17. #19127502 | C22 | semidirect |
| 151. C83 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127739 | 2 |
| #24909668 | 2 |
| #24909651 | 2 |
| #24909252 | 2 |
| #24909175 | 2 |
| #24909074 | 2 |
| C83×#3050 | 2 |
| #33647 | 83 |