Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
622 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #24916931 | C2 | semidirect |
| 2. #24912372 | C2 | semidirect |
| 3. #24906023 | C2 | semidirect |
| 4. #24905888 | C2 | semidirect |
| 5. #24905859 | C2 | semidirect |
| 6. #24905322 | C2 | semidirect |
| 91. C2×Dic166 | D8 | semidirect |
| 251. C83 | #9997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916931 | 2 |
| #24912372 | 2 |
| #24906023 | 2 |
| #24905888 | 2 |
| #24905859 | 2 |
| #24905322 | 2 |
| C83×#3100 | 2 |
| #9997 | 83 |