Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19127997 | C2 | semidirect |
| 4. #24906149 | C2 | semidirect |
| 6. #24905786 | C2 | semidirect |
| 7. C83×#1301 | C2 | semidirect |
| 90. C2×Dic166 | SD16 | semidirect |
| 206. #1301 | D83 | semidirect |
| 207. C83 | #10181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918390 | 2 |
| C2×#19127997 | 2 |
| #24916937 | 2 |
| #24906149 | 2 |
| #24905861 | 2 |
| #24905786 | 2 |
| C83×#1301 | 2 |
| #10181 | 83 |