Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
2014 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 2014 conjugacy classes of subgroups — too many to draw. Only its 355 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. C2×#19127546 | C2 | semidirect |
| 3. #24905733 | C2 | semidirect |
| 5. #24905700 | C2 | semidirect |
| 9. C2×#14581779 | C4 | semidirect |
| 69. C4×Dic83 | C22⋊C4 | semidirect |
| 165. C83 | #14169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581779 | 2 |
| C2×#19127546 | 2 |
| #24905733 | 2 |
| #24905704 | 2 |
| #24905700 | 2 |
| C83×#1438 | 2 |
| #14169 | 83 |