Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24909235 | C2 | semidirect |
| 3. C2×#19127515 | C2 | semidirect |
| 4. #24909178 | C2 | semidirect |
| 5. #24909092 | C2 | semidirect |
| 6. #24907514 | C2 | semidirect |
| 7. C83×#1384 | C2 | semidirect |
| 47. C2×C83⋊C16 | D4 | semidirect |
| 172. #1384 | D83 | semidirect |
| 173. C83 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917112 | 2 |
| #24909235 | 2 |
| C2×#19127515 | 2 |
| #24909178 | 2 |
| #24909092 | 2 |
| #24907514 | 2 |
| C83×#1384 | 2 |
| #13396 | 83 |