Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909750 | C2 | semidirect |
| 3. #24906981 | C2 | semidirect |
| 4. #24905515 | C2 | semidirect |
| 5. #24905445 | C2 | semidirect |
| 74. D8×C83 | Q16 | semidirect |
| 143. C83 | #12414 | semidirect |
| 205. D8 | #13050580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909750 | 2 |
| #24909610 | 2 |
| #24906981 | 2 |
| #24905515 | 2 |
| #24905445 | 2 |
| #24905430 | 2 |
| C83×#3389 | 2 |
| #12414 | 83 |