Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
140 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 6. #15690879 | C4 | semidirect |
| 9. #15690878 | C4 | semidirect |
| 11. #15690750 | C4 | semidirect |
| 14. M32×C97 | C4 | semidirect |
| 59. C97 | #1386 | semidirect |
| 68. M32 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261745 | 2 |
| C2×#15690878 | 2 |
| M32×D97 | 2 |
| #1386 | 97 |