Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. C2×#15690746 | C2 | semidirect |
| 5. #20260690 | C2 | semidirect |
| 6. #20260495 | C2 | semidirect |
| 7. #336×C97 | C2 | semidirect |
| 14. #15690735 | C4 | semidirect |
| 15. #15690735 | C4 | semidirect |
| 16. #15690732 | C4 | semidirect |
| 17. #15690732 | C4 | semidirect |
| 106. C97 | #1929 | semidirect |
| 113. #336 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690746 | 2 |
| C2×#15690738 | 2 |
| #20260732 | 2 |
| #20260701 | 2 |
| #20260690 | 2 |
| #20260495 | 2 |
| #336×C97 | 2 |
| #1929 | 97 |