Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24917995 | C2 | semidirect |
| 4. #24905569 | C2 | semidirect |
| 5. #24905564 | C2 | semidirect |
| 6. #24905548 | C2 | semidirect |
| 52. C2×Q16×C83 | Q8 | semidirect |
| 54. C2×D8×C83 | Q8 | semidirect |
| 164. C83 | #13374 | semidirect |
| 187. C2×Q16 | Dic166 | semidirect |
| 189. C2×D8 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917995 | 2 |
| C2×#19127511 | 2 |
| #24908362 | 2 |
| #24905569 | 2 |
| #24905564 | 2 |
| #24905548 | 2 |
| C83×#2145 | 2 |
| #13374 | 83 |