Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #24907588 | C2 | semidirect |
| 4. #24905578 | C2 | semidirect |
| 5. #24905574 | C2 | semidirect |
| 6. #24905548 | C2 | semidirect |
| 136. C83 | #13490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909179 | 2 |
| #24908374 | 2 |
| #24907588 | 2 |
| #24905578 | 2 |
| #24905574 | 2 |
| #24905548 | 2 |
| C2×#361×C83 | 2 |
| #13490 | 83 |