Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
406 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 101 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. #24905568 | C2 | semidirect |
| 4. #24905547 | C2 | semidirect |
| 5. C83×#3162 | C2 | semidirect |
| 21. C2×D664 | Q8 | semidirect |
| 120. #3162 | D83 | semidirect |
| 125. C83 | #13367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909178 | 2 |
| #24908339 | 2 |
| #24905568 | 2 |
| #24905547 | 2 |
| C83×#3162 | 2 |
| #13367 | 83 |