Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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. #20261626 | C2 | semidirect |
| 4. #20261625 | C2 | semidirect |
| 9. #15690884 | C4 | semidirect |
| 10. #15690883 | C4 | semidirect |
| 16. #15690750 | C4 | semidirect |
| 18. C16×D97 | C4 | semidirect |
| 19. M32×C97 | C4 | semidirect |
| 28. #13095514 | C2×C4 | semidirect |
| 35. #13095486 | C2×C4 | semidirect |
| 37. C16×C97 | C2×C4 | semidirect |
| 67. D97 | #347 | semidirect |
| 69. C97 | C2×#347 | semidirect |
| 82. M32 | #87604 | semidirect |
| 106. C16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| C2×#15690864 | 2 |
| #20261626 | 2 |
| #20261625 | 2 |
| M32×D97 | 2 |
| C2×#347 | 97 |