Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
498 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909128 | C2 | semidirect |
| 3. #24905615 | C2 | semidirect |
| 4. C83×#1525 | C2 | semidirect |
| 5. #19128537 | C4 | semidirect |
| 7. #19127883 | C4 | semidirect |
| 12. #19127685 | C4 | semidirect |
| 14. #19127496 | C22 | semidirect |
| 19. #329×C83 | C22 | semidirect |
| 177. #1525 | D83 | semidirect |
| 179. C83 | #13568 | semidirect |
| 194. #329 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916811 | 2 |
| #24909128 | 2 |
| #24905615 | 2 |
| C83×#1525 | 2 |
| #13568 | 83 |