Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24916182 | C2 | semidirect |
| 3. #24908261 | C2 | semidirect |
| 4. #24906110 | C2 | semidirect |
| 5. #24905889 | C2 | semidirect |
| 6. #24905359 | C2 | semidirect |
| 7. C83×#1281 | C2 | semidirect |
| 121. C2×C8×C83 | D8 | semidirect |
| 214. #1281 | D83 | semidirect |
| 215. C83 | #9049 | semidirect |
| 321. C2×C8 | D664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917464 | 2 |
| #24916182 | 2 |
| #24908261 | 2 |
| #24906110 | 2 |
| #24905889 | 2 |
| #24905359 | 2 |
| C83×#1281 | 2 |
| #9049 | 83 |