Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
306 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 11. #19128101 | C4 | semidirect |
| 12. #19128098 | C4 | semidirect |
| 34. C2×C83⋊C16 | Q8 | semidirect |
| 47. M32×C83 | Q8 | semidirect |
| 131. C83 | #13291 | semidirect |
| 162. M32 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917995 | 2 |
| #24909067 | 2 |
| #24907588 | 2 |
| #24905569 | 2 |
| #24905564 | 2 |
| #24905563 | 2 |
| C83×#1389 | 2 |
| #13291 | 83 |