Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1386 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 243 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. #24916092 | C2 | semidirect |
| 3. #24908311 | C2 | semidirect |
| 4. #24907387 | C2 | semidirect |
| 6. C83×#1784 | C2 | semidirect |
| 16. #19127724 | C22 | semidirect |
| 17. C2×#14581711 | C22 | semidirect |
| 20. M16×Dic83 | C22 | semidirect |
| 22. C2×#101×C83 | C22 | semidirect |
| 158. #1784 | D83 | semidirect |
| 160. C83 | #21798 | semidirect |
| 173. C2×#101 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581781 | 2 |
| #24916092 | 2 |
| #24908311 | 2 |
| #24907387 | 2 |
| #24907383 | 2 |
| C83×#1784 | 2 |
| #21798 | 83 |