Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 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 |
|---|---|---|
| 12. Dic776 | C4 | semidirect |
| 13. #15690756 | C4 | semidirect |
| 15. Q32×C97 | C4 | semidirect |
| 43. #87604 | Q32 | direct (N × H) |
| 52. C97 | C4×Q32 | semidirect |
| 62. Q32 | #87604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#87604 | 2 |
| #20261661 | 2 |
| #20261648 | 2 |
| C16×#87604 | 2 |
| Q32×D97 | 2 |
| C4×Q32 | 97 |