Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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. C4×#11715895 | C4 | semidirect |
| 13. C8×Dic97 | C4 | semidirect |
| 14. C8×Dic97 | C4 | semidirect |
| 15. C4×C8×C97 | C4 | semidirect |
| 64. C97 | #1846 | semidirect |
| 78. C4×C8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690879 | 2 |
| C2×#15690878 | 2 |
| #20261679 | 2 |
| C4×C8×D97 | 2 |
| #1846 | 97 |