Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
316 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 97 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. #24909258 | C2 | semidirect |
| 5. C4×#14581728 | C2 | semidirect |
| 6. #24905575 | C2 | semidirect |
| 7. C83×#1376 | C2 | semidirect |
| 16. #19127518 | C4 | semidirect |
| 17. #19127515 | C4 | semidirect |
| 148. #1376 | D83 | semidirect |
| 149. C83 | #13137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909258 | 2 |
| #24909213 | 2 |
| #24909192 | 2 |
| #24908351 | 2 |
| C4×#14581728 | 2 |
| #24905575 | 2 |
| C83×#1376 | 2 |
| #13137 | 83 |