Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
356 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 356 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. #24908236 | C2 | semidirect |
| 5. #24905753 | C2 | semidirect |
| 6. #24905304 | C2 | semidirect |
| 7. C83×#1303 | C2 | semidirect |
| 16. #19127446 | C4 | semidirect |
| 17. #19127446 | C4 | semidirect |
| 18. #19127444 | C4 | semidirect |
| 19. #19127444 | C4 | semidirect |
| 175. #1303 | D83 | semidirect |
| 177. C83 | #9592 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908381 | 2 |
| #24908236 | 2 |
| #24906110 | 2 |
| #24905913 | 2 |
| #24905753 | 2 |
| #24905304 | 2 |
| C83×#1303 | 2 |
| #9592 | 83 |