Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
284 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 55 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. #24909783 | C2 | semidirect |
| 3. C2×#19127539 | C2 | semidirect |
| 4. #24909589 | C2 | semidirect |
| 5. #24905646 | C2 | semidirect |
| 6. #24905606 | C2 | semidirect |
| 7. C83×#1419 | C2 | semidirect |
| 13. C2×Dic664 | C22 | semidirect |
| 20. C2×C83⋊C32 | C22 | semidirect |
| 23. M64×C83 | C22 | semidirect |
| 24. #368×C83 | C22 | semidirect |
| 124. #1419 | D83 | semidirect |
| 127. C83 | #13671 | semidirect |
| 141. M64 | C2×D83 | semidirect |
| 143. #368 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920600 | 2 |
| #24909783 | 2 |
| C2×#19127539 | 2 |
| #24909589 | 2 |
| #24905646 | 2 |
| #24905606 | 2 |
| C83×#1419 | 2 |
| #13671 | 83 |