Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24908236 | C2 | semidirect |
| 3. #24906145 | C2 | semidirect |
| 4. C2×#19127448 | C2 | semidirect |
| 6. #24905313 | C2 | semidirect |
| 180. C83 | #10552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917856 | 2 |
| #24908236 | 2 |
| #24906145 | 2 |
| C2×#19127448 | 2 |
| #24905862 | 2 |
| #24905313 | 2 |
| C83×#1547 | 2 |
| #10552 | 83 |