Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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. #24909737 | C2 | semidirect |
| 3. #24905662 | C2 | semidirect |
| 4. Dic83⋊C32 | C2 | semidirect |
| 7. C83×#1423 | C2 | semidirect |
| 23. D1328 | Q8 | semidirect |
| 83. #1423 | D83 | semidirect |
| 87. C83 | #13703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909737 | 2 |
| #24909309 | 2 |
| #24905662 | 2 |
| Dic83⋊C32 | 2 |
| #24905642 | 2 |
| #24905640 | 2 |
| C83×#1423 | 2 |
| #13703 | 83 |