Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
442 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 442 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 |
|---|---|---|
| 2. #24909719 | C2 | semidirect |
| 3. #24909508 | C2 | semidirect |
| 4. #24906829 | C2 | semidirect |
| 5. #24905508 | C2 | semidirect |
| 6. #24905419 | C2 | semidirect |
| 7. C83×#1331 | C2 | semidirect |
| 12. #19128081 | C22 | semidirect |
| 19. C4⋊(C83⋊C16) | C22 | semidirect |
| 23. C4×C16×C83 | C22 | semidirect |
| 24. #335×C83 | C22 | semidirect |
| 120. D332 | SD32 | semidirect |
| 161. #1331 | D83 | semidirect |
| 163. C83 | #12320 | semidirect |
| 178. C4×C16 | C2×D83 | semidirect |
| 179. #335 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D332 | 2 |
| #24909719 | 2 |
| #24909508 | 2 |
| #24906829 | 2 |
| #24905508 | 2 |
| #24905419 | 2 |
| C83×#1331 | 2 |
| #12320 | 83 |