Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
366 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19128098 | C4 | semidirect |
| 33. #14581726 | Q8 | semidirect |
| 49. #108×C83 | Q8 | semidirect |
| 129. C83 | #13272 | semidirect |
| 162. #108 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128098 | 2 |
| C2×#19127521 | 2 |
| #24907345 | 2 |
| #24905570 | 2 |
| #24905569 | 2 |
| #24905563 | 2 |
| C83×#1383 | 2 |
| #13272 | 83 |