Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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. #24906978 | C2 | semidirect |
| 4. #24905515 | C2 | semidirect |
| 5. #24905446 | C2 | semidirect |
| 7. C83×#2255 | C2 | semidirect |
| 68. D664 | Q16 | semidirect |
| 137. #2255 | D83 | semidirect |
| 143. C83 | #12414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920424 | 2 |
| #24909607 | 2 |
| #24906978 | 2 |
| #24905515 | 2 |
| #24905446 | 2 |
| #24905431 | 2 |
| C83×#2255 | 2 |
| #12414 | 83 |