Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 3. #24907580 | C2 | semidirect |
| 4. #24906153 | C2 | semidirect |
| 6. #24905337 | C2 | semidirect |
| 7. C83×#1994 | C2 | semidirect |
| 114. C42×C83 | SD16 | semidirect |
| 191. #1994 | D83 | semidirect |
| 197. C83 | #10521 | semidirect |
| 304. C42 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918775 | 2 |
| #24908291 | 2 |
| #24907580 | 2 |
| #24906153 | 2 |
| #24906141 | 2 |
| #24905337 | 2 |
| C83×#1994 | 2 |
| #10521 | 83 |