Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
554 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24915840 | C2 | semidirect |
| 5. #24906145 | C2 | semidirect |
| 6. #24905295 | C2 | semidirect |
| 7. C83×#1546 | C2 | semidirect |
| 180. #1546 | D83 | semidirect |
| 182. C83 | #10288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918584 | 2 |
| #24918390 | 2 |
| #24915840 | 2 |
| #24908290 | 2 |
| #24906145 | 2 |
| #24905295 | 2 |
| C83×#1546 | 2 |
| #10288 | 83 |