Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
328 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 328 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 |
|---|---|---|
| 3. C2×#19127478 | C2 | semidirect |
| 5. #24908199 | C2 | semidirect |
| 6. #24905573 | C2 | semidirect |
| 7. C83×#1383 | C2 | semidirect |
| 16. #19127506 | C4 | semidirect |
| 17. #19127503 | C4 | semidirect |
| 155. #1383 | D83 | semidirect |
| 156. C83 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127510 | 2 |
| #24909176 | 2 |
| C2×#19127478 | 2 |
| #24908354 | 2 |
| #24908199 | 2 |
| #24905573 | 2 |
| C83×#1383 | 2 |
| #13153 | 83 |