Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#13095500 | C2 | semidirect |
| 3. #20261311 | C2 | semidirect |
| 4. #20261209 | C2 | semidirect |
| 5. #20260951 | C2 | semidirect |
| 6. #20260941 | C2 | semidirect |
| 7. #20260745 | C2 | semidirect |
| 8. #20260732 | C2 | semidirect |
| 9. #424×C97 | C2 | semidirect |
| 18. #15690810 | C22 | semidirect |
| 19. #15690798 | C22 | semidirect |
| 26. #15690735 | C22 | semidirect |
| 27. #15690735 | C22 | semidirect |
| 28. #15690732 | C22 | semidirect |
| 32. C4⋊C8×C97 | C22 | semidirect |
| 117. C97 | #3042 | semidirect |
| 124. #424 | D97 | semidirect |
| 146. C4⋊C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690838 | 2 |
| C22×#13095500 | 2 |
| #20261311 | 2 |
| #20261209 | 2 |
| #20260951 | 2 |
| #20260941 | 2 |
| #20260745 | 2 |
| #20260732 | 2 |
| #424×C97 | 2 |
| #3042 | 97 |