Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #24910276 | C2 | semidirect |
| 3. #24906060 | C2 | semidirect |
| 4. #24906010 | C2 | semidirect |
| 5. #24905328 | C2 | semidirect |
| 6. #24905319 | C2 | semidirect |
| 7. C83×#1980 | C2 | semidirect |
| 9. #19128088 | C4 | semidirect |
| 10. #19128063 | C4 | semidirect |
| 54. #14581703 | C2×C4 | semidirect |
| 63. C4⋊Q8×C83 | C2×C4 | semidirect |
| 64. #127×C83 | C2×C4 | semidirect |
| 224. #1980 | D83 | semidirect |
| 229. C83 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D83 | semidirect |
| 261. #127 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918446 | 2 |
| #24910276 | 2 |
| #24906060 | 2 |
| #24906010 | 2 |
| #24905328 | 2 |
| #24905319 | 2 |
| C83×#1980 | 2 |
| #9381 | 83 |