Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×Dic166 | C2 | semidirect |
| 2. #24909687 | C2 | semidirect |
| 4. #24906824 | C2 | semidirect |
| 5. #24905519 | C2 | semidirect |
| 6. #24905443 | C2 | semidirect |
| 7. C83×#1331 | C2 | semidirect |
| 78. D8×C83 | SD16 | semidirect |
| 109. Dic166 | D16 | semidirect |
| 143. #1331 | D83 | semidirect |
| 144. C83 | #12352 | semidirect |
| 206. D8 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic166 | 2 |
| #24909687 | 2 |
| #24909498 | 2 |
| #24906824 | 2 |
| #24905519 | 2 |
| #24905443 | 2 |
| C83×#1331 | 2 |
| #12352 | 83 |