Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 3. #24905670 | C2 | semidirect |
| 4. #24905669 | C2 | semidirect |
| 5. #24905656 | C2 | semidirect |
| 7. C83×#1420 | C2 | semidirect |
| 85. #1420 | D83 | semidirect |
| 87. C83 | #13718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909568 | 2 |
| #24909256 | 2 |
| #24905670 | 2 |
| #24905669 | 2 |
| #24905656 | 2 |
| #24905602 | 2 |
| C83×#1420 | 2 |
| #13718 | 83 |