Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24907499 | C2 | semidirect |
| 3. #24907242 | C2 | semidirect |
| 4. #24905980 | C2 | semidirect |
| 5. #24905979 | C2 | semidirect |
| 6. #24905822 | C2 | semidirect |
| 7. C83×#1471 | C2 | semidirect |
| 8. C22×#13050575 | C4 | semidirect |
| 16. C2×#14581725 | C4 | semidirect |
| 17. C2×#14581713 | C4 | semidirect |
| 18. C2×#14581712 | C4 | semidirect |
| 231. #1471 | D83 | semidirect |
| 232. C83 | #9818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127935 | 2 |
| #24907499 | 2 |
| #24907242 | 2 |
| #24905980 | 2 |
| #24905979 | 2 |
| #24905822 | 2 |
| C83×#1471 | 2 |
| #9818 | 83 |