Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24909258 | C2 | semidirect |
| 4. #24908254 | C2 | semidirect |
| 5. #24905556 | C2 | semidirect |
| 6. #24905553 | C2 | semidirect |
| 23. #362×C83 | C4 | semidirect |
| 24. #361×C83 | C4 | semidirect |
| 149. C83 | #12942 | semidirect |
| 163. #362 | Dic83 | semidirect |
| 164. #361 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916380 | 2 |
| #24909258 | 2 |
| C2×#19127508 | 2 |
| #24908254 | 2 |
| #24905556 | 2 |
| #24905553 | 2 |
| C83×#2148 | 2 |
| #12942 | 83 |