Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24907582 | C2 | semidirect |
| 5. #24905355 | C2 | semidirect |
| 6. #24905312 | C2 | semidirect |
| 7. C83×#1573 | C2 | semidirect |
| 179. #1573 | D83 | semidirect |
| 184. C83 | #8877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916604 | 2 |
| #24907582 | 2 |
| #24905950 | 2 |
| #24905874 | 2 |
| #24905355 | 2 |
| #24905312 | 2 |
| C83×#1573 | 2 |
| #8877 | 83 |