Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #20261502 | C2 | semidirect |
| 3. #20260753 | C2 | semidirect |
| 4. C2×#15690738 | C2 | semidirect |
| 5. C4×#41×C97 | C2 | semidirect |
| 7. #15690857 | C4 | semidirect |
| 8. #15690856 | C4 | semidirect |
| 13. C2×#13095495 | C22 | semidirect |
| 14. #15690738 | C22 | semidirect |
| 15. #15690738 | C22 | semidirect |
| 19. #117×C97 | C22 | semidirect |
| 20. C2×C42×C97 | C22 | semidirect |
| 24. #13095511 | C2×C4 | semidirect |
| 27. C2×Dic194 | C2×C4 | semidirect |
| 29. C2×D388 | C2×C4 | semidirect |
| 84. C97 | #2901 | semidirect |
| 87. C4×#41 | D97 | semidirect |
| 101. #117 | C2×D97 | semidirect |
| 102. C2×C42 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261571 | 2 |
| #20261502 | 2 |
| #20260753 | 2 |
| C2×#15690738 | 2 |
| C4×#41×C97 | 2 |
| #2901 | 97 |