Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
562 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19128097 | C2 | semidirect |
| 4. #24906136 | C2 | semidirect |
| 6. #24905301 | C2 | semidirect |
| 7. C83×#1997 | C2 | semidirect |
| 176. #1997 | D83 | semidirect |
| 180. C83 | #10172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918591 | 2 |
| C2×#19128097 | 2 |
| #24917922 | 2 |
| #24906136 | 2 |
| #24905913 | 2 |
| #24905301 | 2 |
| C83×#1997 | 2 |
| #10172 | 83 |