Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
398 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24916568 | C2 | semidirect |
| 3. #24906127 | C2 | semidirect |
| 5. #24905363 | C2 | semidirect |
| 6. #24905361 | C2 | semidirect |
| 156. C83 | #9008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917808 | 2 |
| #24916568 | 2 |
| #24906127 | 2 |
| #24905932 | 2 |
| #24905363 | 2 |
| #24905361 | 2 |
| C83×#1496 | 2 |
| #9008 | 83 |