Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1124 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×Dic332 | C2 | semidirect |
| 2. C2×#19128144 | C2 | semidirect |
| 4. #24909399 | C2 | semidirect |
| 5. #24909382 | C2 | semidirect |
| 6. #24909184 | C2 | semidirect |
| 7. C83×#2112 | C2 | semidirect |
| 17. C2×Dic664 | C22 | semidirect |
| 18. C2×#14581737 | C22 | semidirect |
| 24. #19127506 | C22 | semidirect |
| 43. C2×Dic332 | D4 | semidirect |
| 153. C22×C83 | #510 | semidirect |
| 176. #2112 | D83 | semidirect |
| 177. C83 | #33518 | semidirect |
| 325. C22 | #19128144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic332 | 2 |
| C2×#19128144 | 2 |
| #24917044 | 2 |
| #24909399 | 2 |
| #24909382 | 2 |
| #24909184 | 2 |
| C83×#2112 | 2 |
| #33518 | 83 |