Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
530 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24908284 | C2 | semidirect |
| 5. #24905345 | C2 | semidirect |
| 6. #24905344 | C2 | semidirect |
| 7. C83×#1993 | C2 | semidirect |
| 10. #19128063 | C4 | semidirect |
| 55. #14581703 | C2×C4 | semidirect |
| 65. C4⋊Q8×C83 | C2×C4 | semidirect |
| 219. #1993 | D83 | semidirect |
| 224. C83 | #8999 | semidirect |
| 257. C4⋊Q8 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128063 | 2 |
| #24910634 | 2 |
| #24908284 | 2 |
| C2×#19127440 | 2 |
| #24905345 | 2 |
| #24905344 | 2 |
| C83×#1993 | 2 |
| #8999 | 83 |