Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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×#19127518 | C2 | semidirect |
| 4. #24908378 | C2 | semidirect |
| 6. #24905557 | C2 | semidirect |
| 7. C83×#2151 | C2 | semidirect |
| 155. #2151 | D83 | semidirect |
| 161. C83 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581737 | 2 |
| C2×#19127518 | 2 |
| C2×#19127515 | 2 |
| #24908378 | 2 |
| #24908373 | 2 |
| #24905557 | 2 |
| C83×#2151 | 2 |
| #13440 | 83 |