Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 468 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 |
|---|---|---|
| 1. #24909135 | C2 | semidirect |
| 2. #24909113 | C2 | semidirect |
| 3. #24907509 | C2 | semidirect |
| 4. #24907263 | C2 | semidirect |
| 15. C22×D8×C83 | C4 | semidirect |
| 22. #427×C83 | C4 | semidirect |
| 23. #418×C83 | C4 | semidirect |
| 173. C83 | #13231 | semidirect |
| 174. C22×D8 | Dic83 | semidirect |
| 182. #427 | Dic83 | semidirect |
| 183. #418 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909135 | 2 |
| #24909113 | 2 |
| #24907509 | 2 |
| #24907263 | 2 |
| C83×#3058 | 2 |
| #13231 | 83 |