Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
176 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 59 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. #24905665 | C2 | semidirect |
| 4. #24905664 | C2 | semidirect |
| 5. Dic83⋊C32 | C2 | semidirect |
| 30. D16×C83 | Q8 | semidirect |
| 87. C83 | #13705 | semidirect |
| 103. D16 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909737 | 2 |
| D16×Dic83 | 2 |
| #24905665 | 2 |
| #24905664 | 2 |
| Dic83⋊C32 | 2 |
| #24905641 | 2 |
| C83×#1415 | 2 |
| #13705 | 83 |