Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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. #24906238 | C2 | semidirect |
| 4. #24906135 | C2 | semidirect |
| 6. #24905358 | C2 | semidirect |
| 7. C83×#1546 | C2 | semidirect |
| 175. #1546 | D83 | semidirect |
| 178. C83 | #10444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127903 | 2 |
| #24907452 | 2 |
| #24906238 | 2 |
| #24906135 | 2 |
| #24905853 | 2 |
| #24905358 | 2 |
| C83×#1546 | 2 |
| #10444 | 83 |