Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
588 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #24909924 | C2 | semidirect |
| 3. #24908290 | C2 | semidirect |
| 4. #24905957 | C2 | semidirect |
| 5. #24905887 | C2 | semidirect |
| 6. #24905295 | C2 | semidirect |
| 7. C83×#1303 | C2 | semidirect |
| 12. #19127982 | C4 | semidirect |
| 13. #19127897 | C4 | semidirect |
| 115. C4×Dic83 | D8 | semidirect |
| 222. #1303 | D83 | semidirect |
| 224. C83 | #9237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917464 | 2 |
| #24909924 | 2 |
| #24908290 | 2 |
| #24905957 | 2 |
| #24905887 | 2 |
| #24905295 | 2 |
| C83×#1303 | 2 |
| #9237 | 83 |