Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1546 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 1546 conjugacy classes of subgroups — too many to draw. Only its 355 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. #24907535 | C2 | semidirect |
| 4. #24907195 | C2 | semidirect |
| 8. C2×D4×Dic83 | C4 | semidirect |
| 135. C83 | #20690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128176 | 2 |
| #24910045 | 2 |
| #24907535 | 2 |
| #24907195 | 2 |
| C83×#2309 | 2 |
| #20690 | 83 |