Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24907668 | C2 | semidirect |
| 3. #24907646 | C2 | semidirect |
| 5. #24905349 | C2 | semidirect |
| 6. #24905311 | C2 | semidirect |
| 22. #19127438 | C4 | semidirect |
| 23. #19127438 | C4 | semidirect |
| 24. #19127435 | C4 | semidirect |
| 25. #19127435 | C4 | semidirect |
| 225. C83 | #8875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916511 | 2 |
| #24907668 | 2 |
| #24907646 | 2 |
| #24905954 | 2 |
| #24905349 | 2 |
| #24905311 | 2 |
| C83×#1871 | 2 |
| #8875 | 83 |