Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20261361 | C2 | semidirect |
| 4. #20260502 | C2 | semidirect |
| 5. #20260501 | C2 | semidirect |
| 6. #20260501 | C2 | semidirect |
| 36. C24×C97 | Q8 | semidirect |
| 46. C22×C4×C97 | Q8 | semidirect |
| 118. C97 | #2032 | semidirect |
| 139. C24 | Dic194 | semidirect |
| 154. C22×C4 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261361 | 2 |
| C2×#15690725 | 2 |
| #20260502 | 2 |
| #20260501 | 2 |
| C2×#99×C97 | 2 |
| #2032 | 97 |