Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
380 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 55 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. #24915639 | C2 | semidirect |
| 4. #24905489 | C2 | semidirect |
| 5. #24905468 | C2 | semidirect |
| 6. #24905397 | C2 | semidirect |
| 184. C83 | #12201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915639 | 2 |
| #24906500 | 2 |
| #24906466 | 2 |
| #24905489 | 2 |
| #24905468 | 2 |
| #24905397 | 2 |
| C83×#2007 | 2 |
| #12201 | 83 |