Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#19127534 | C2 | semidirect |
| 2. #24909551 | C2 | semidirect |
| 4. #24905663 | C2 | semidirect |
| 5. #24905644 | C2 | semidirect |
| 6. #24905641 | C2 | semidirect |
| 7. C2×SD64×C83 | C2 | semidirect |
| 39. C32×C83 | D4 | semidirect |
| 96. C2×SD64 | D83 | semidirect |
| 103. C83 | #13699 | semidirect |
| 135. C32 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127534 | 2 |
| #24909551 | 2 |
| #24909546 | 2 |
| #24905663 | 2 |
| #24905644 | 2 |
| #24905641 | 2 |
| C2×SD64×C83 | 2 |
| #13699 | 83 |