Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
372 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 65 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. #24909700 | C2 | semidirect |
| 3. #24909610 | C2 | semidirect |
| 4. #24906977 | C2 | semidirect |
| 5. #24905505 | C2 | semidirect |
| 6. #24905422 | C2 | semidirect |
| 7. C83×#1333 | C2 | semidirect |
| 10. #19128106 | C22 | semidirect |
| 19. C4⋊(C83⋊C16) | C22 | semidirect |
| 25. #346×C83 | C22 | semidirect |
| 26. #334×C83 | C22 | semidirect |
| 99. D8×C83 | SD16 | semidirect |
| 172. #1333 | D83 | semidirect |
| 174. C83 | #12378 | semidirect |
| 191. #346 | C2×D83 | semidirect |
| 192. #334 | C2×D83 | semidirect |
| 253. D8 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24919073 | 2 |
| #24909700 | 2 |
| #24909610 | 2 |
| #24906977 | 2 |
| #24905505 | 2 |
| #24905422 | 2 |
| C83×#1333 | 2 |
| #12378 | 83 |