Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. C2×#19128132 | C2 | semidirect |
| 2. #24917892 | C2 | semidirect |
| 3. #24917890 | C2 | semidirect |
| 4. #24909723 | C2 | semidirect |
| 5. #24909719 | C2 | semidirect |
| 6. #24909715 | C2 | semidirect |
| 7. #24909712 | C2 | semidirect |
| 8. C4×C16×D83 | C2 | semidirect |
| 9. C83×#2248 | C2 | semidirect |
| 65. C16×D83 | D4 | semidirect |
| 159. C4×C83 | #508 | semidirect |
| 176. #2248 | D83 | semidirect |
| 180. C83 | #33713 | semidirect |
| 333. C4 | #19128132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128132 | 2 |
| #24917892 | 2 |
| #24917890 | 2 |
| #24909723 | 2 |
| #24909719 | 2 |
| #24909715 | 2 |
| #24909712 | 2 |
| C4×C16×D83 | 2 |
| C83×#2248 | 2 |
| #33713 | 83 |