Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24907318 | C2 | semidirect |
| 3. #24906234 | C2 | semidirect |
| 5. #24905360 | C2 | semidirect |
| 6. #24905295 | C2 | semidirect |
| 21. #332×C83 | C4 | semidirect |
| 22. #331×C83 | C4 | semidirect |
| 163. C83 | #9582 | semidirect |
| 176. #332 | Dic83 | semidirect |
| 177. #331 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908292 | 2 |
| #24907318 | 2 |
| #24906234 | 2 |
| #24905862 | 2 |
| #24905360 | 2 |
| #24905295 | 2 |
| C83×#1540 | 2 |
| #9582 | 83 |