Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #24907080 | C2 | semidirect |
| 5. #24905532 | C2 | semidirect |
| 6. #24905522 | C2 | semidirect |
| 7. C83×#1365 | C2 | semidirect |
| 49. D664 | Q16 | semidirect |
| 110. #1365 | D83 | semidirect |
| 111. C83 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909611 | 2 |
| #24909607 | 2 |
| #24907080 | 2 |
| #24906257 | 2 |
| #24905532 | 2 |
| #24905522 | 2 |
| C83×#1365 | 2 |
| #12447 | 83 |