Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
236 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 75 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. #24909716 | C2 | semidirect |
| 3. #24905535 | C2 | semidirect |
| 4. #24905513 | C2 | semidirect |
| 56. D4×C83 | Q32 | semidirect |
| 92. C83 | #12431 | semidirect |
| 145. D4 | Dic664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909716 | 2 |
| #24906828 | 2 |
| #24905535 | 2 |
| #24905513 | 2 |
| D4×C16×C83 | 2 |
| #12431 | 83 |