Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19127527 | C2 | semidirect |
| 5. #24908248 | C2 | semidirect |
| 6. #24905572 | C2 | semidirect |
| 7. C83×#1379 | C2 | semidirect |
| 19. #19127509 | C4 | semidirect |
| 43. #14581728 | C2×C4 | semidirect |
| 60. C2×C16×C83 | C2×C4 | semidirect |
| 166. #1379 | D83 | semidirect |
| 167. C83 | #12945 | semidirect |
| 210. C2×C16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916340 | 2 |
| C2×#19127527 | 2 |
| C2×#19127509 | 2 |
| #24909176 | 2 |
| #24908248 | 2 |
| #24905572 | 2 |
| C83×#1379 | 2 |
| #12945 | 83 |