Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #24905521 | C2 | semidirect |
| 5. Q8⋊(C83⋊C16) | C2 | semidirect |
| 6. #24905427 | C2 | semidirect |
| 7. Q8×Q16×C83 | C2 | semidirect |
| 68. Q16×C83 | SD16 | semidirect |
| 90. Q8×C83 | SD32 | semidirect |
| 128. Q8×Q16 | D83 | semidirect |
| 135. C83 | #12354 | semidirect |
| 189. Q16 | #13050577 | semidirect |
| 218. Q8 | #14581735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909688 | 2 |
| #24909503 | 2 |
| #24906823 | 2 |
| #24905521 | 2 |
| Q8⋊(C83⋊C16) | 2 |
| #24905427 | 2 |
| Q8×Q16×C83 | 2 |
| #12354 | 83 |