Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #24906235 | C2 | semidirect |
| 4. #24906148 | C2 | semidirect |
| 6. #24905359 | C2 | semidirect |
| 7. C83×#1548 | C2 | semidirect |
| 166. #1548 | D83 | semidirect |
| 169. C83 | #10448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127978 | 2 |
| #24907452 | 2 |
| #24906235 | 2 |
| #24906148 | 2 |
| #24905855 | 2 |
| #24905359 | 2 |
| C83×#1548 | 2 |
| #10448 | 83 |