Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
644 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24907398 | C2 | semidirect |
| 3. #24907387 | C2 | semidirect |
| 5. #24905370 | C2 | semidirect |
| 6. #24905339 | C2 | semidirect |
| 28. #451×C83 | C4 | semidirect |
| 30. #448×C83 | C4 | semidirect |
| 258. C83 | #9519 | semidirect |
| 263. #451 | Dic83 | semidirect |
| 265. #448 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916511 | 2 |
| #24907398 | 2 |
| #24907387 | 2 |
| #24906006 | 2 |
| #24905370 | 2 |
| #24905339 | 2 |
| C83×#3004 | 2 |
| #9519 | 83 |