Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
170 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #24909742 | C2 | semidirect |
| 3. #24905665 | C2 | semidirect |
| 4. #24905663 | C2 | semidirect |
| 7. C83×C4⋊C32 | C2 | semidirect |
| 83. C4⋊C32 | D83 | semidirect |
| 86. C83 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909742 | 2 |
| C4×D1328 | 2 |
| #24905665 | 2 |
| #24905663 | 2 |
| #24905642 | 2 |
| C83×C4⋊C32 | 2 |
| #13707 | 83 |