Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
316 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 1. #24909736 | C2 | semidirect |
| 3. #24906857 | C2 | semidirect |
| 4. #24905518 | C2 | semidirect |
| 5. Q8⋊(C83⋊C16) | C2 | semidirect |
| 68. D8×C83 | Q16 | semidirect |
| 134. C83 | #12404 | semidirect |
| 190. D8 | #13050580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909736 | 2 |
| #24909600 | 2 |
| #24906857 | 2 |
| #24905518 | 2 |
| Q8⋊(C83⋊C16) | 2 |
| #24905424 | 2 |
| Q8×D8×C83 | 2 |
| #12404 | 83 |