Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24915839 | C2 | semidirect |
| 4. #24905322 | C2 | semidirect |
| 5. #24905321 | C2 | semidirect |
| 6. #24905295 | C2 | semidirect |
| 44. C4⋊Q8×C83 | Q8 | semidirect |
| 45. #127×C83 | Q8 | semidirect |
| 178. C83 | #10362 | semidirect |
| 199. C4⋊Q8 | Dic166 | semidirect |
| 200. #127 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24915839 | 2 |
| #24908292 | 2 |
| #24906023 | 2 |
| #24905322 | 2 |
| #24905321 | 2 |
| #24905295 | 2 |
| C83×#1517 | 2 |
| #10362 | 83 |