Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
482 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 97 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. #24906224 | C2 | semidirect |
| 3. #24906060 | C2 | semidirect |
| 4. #24905816 | C2 | semidirect |
| 5. #24905815 | C2 | semidirect |
| 6. M16×C83⋊C8 | C2 | semidirect |
| 7. C83×#1527 | C2 | semidirect |
| 206. #1527 | D83 | semidirect |
| 210. C83 | #9787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128083 | 2 |
| #24906224 | 2 |
| #24906060 | 2 |
| #24905816 | 2 |
| #24905815 | 2 |
| M16×C83⋊C8 | 2 |
| C83×#1527 | 2 |
| #9787 | 83 |