Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
458 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24908291 | C2 | semidirect |
| 3. #24907580 | C2 | semidirect |
| 4. #24906141 | C2 | semidirect |
| 5. #24906140 | C2 | semidirect |
| 6. #24905337 | C2 | semidirect |
| 7. C83×#1962 | C2 | semidirect |
| 120. C42×C83 | D8 | semidirect |
| 209. #1962 | D83 | semidirect |
| 214. C83 | #10519 | semidirect |
| 327. C42 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918770 | 2 |
| #24908291 | 2 |
| #24907580 | 2 |
| #24906141 | 2 |
| #24906140 | 2 |
| #24905337 | 2 |
| C83×#1962 | 2 |
| #10519 | 83 |