Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24909249 | C2 | semidirect |
| 5. #24905571 | C2 | semidirect |
| 6. #24905559 | C2 | semidirect |
| 7. C2×#366×C83 | C2 | semidirect |
| 20. #19127484 | C4 | semidirect |
| 42. #14581732 | C2×C4 | semidirect |
| 58. C2×C16×C83 | C2×C4 | semidirect |
| 160. C2×#366 | D83 | semidirect |
| 165. C83 | #12925 | semidirect |
| 207. C2×C16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916059 | 2 |
| #24909249 | 2 |
| C2×#19127484 | 2 |
| #24907528 | 2 |
| #24905571 | 2 |
| #24905559 | 2 |
| C2×#366×C83 | 2 |
| #12925 | 83 |