Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×D664 | C2 | semidirect |
| 2. #24909686 | C2 | semidirect |
| 4. #24905519 | C2 | semidirect |
| 5. Q8⋊(C83⋊C16) | C2 | semidirect |
| 6. #24905423 | C2 | semidirect |
| 7. C83×#1668 | C2 | semidirect |
| 61. D664 | SD16 | semidirect |
| 89. Q8×C83 | D16 | semidirect |
| 140. #1668 | D83 | semidirect |
| 144. C83 | #12352 | semidirect |
| 229. Q8 | #14581733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D664 | 2 |
| #24909686 | 2 |
| #24909495 | 2 |
| #24905519 | 2 |
| Q8⋊(C83⋊C16) | 2 |
| #24905423 | 2 |
| C83×#1668 | 2 |
| #12352 | 83 |