Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 2. #24909738 | C2 | semidirect |
| 4. #24906857 | C2 | semidirect |
| 5. #24905517 | C2 | semidirect |
| 7. C83×Q8⋊C16 | C2 | semidirect |
| 62. D664 | Q16 | semidirect |
| 132. Q8⋊C16 | D83 | semidirect |
| 134. C83 | #12404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D664 | 2 |
| #24909738 | 2 |
| #24909601 | 2 |
| #24906857 | 2 |
| #24905517 | 2 |
| #24905425 | 2 |
| C83×Q8⋊C16 | 2 |
| #12404 | 83 |