Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 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 |
|---|---|---|
| 1. C2×#19127540 | C2 | semidirect |
| 2. C2×#19127539 | C2 | semidirect |
| 3. C2×#19127536 | C2 | semidirect |
| 4. #24909721 | C2 | semidirect |
| 5. #24909711 | C2 | semidirect |
| 6. #24905596 | C2 | semidirect |
| 7. C2×D32×C83 | C2 | semidirect |
| 37. C83⋊C32 | D4 | semidirect |
| 45. C32×C83 | D4 | semidirect |
| 106. C2×D32 | D83 | semidirect |
| 110. C83 | #13729 | semidirect |
| 148. C32 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127540 | 2 |
| C2×#19127539 | 2 |
| C2×#19127536 | 2 |
| #24909721 | 2 |
| #24909711 | 2 |
| #24905596 | 2 |
| C2×D32×C83 | 2 |
| #13729 | 83 |