Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 10. #15690721 | C4 | semidirect |
| 11. #15690720 | C4 | semidirect |
| 12. C8×Dic97 | C4 | semidirect |
| 15. #97×C97 | C4 | semidirect |
| 42. C8×C97 | C42 | semidirect |
| 43. #11715895 | C42 | semidirect |
| 52. Dic97 | #97 | direct (N × H) |
| 58. C97 | C4×#97 | semidirect |
| 72. #97 | Dic97 | direct (N × H) |
| 101. C8 | C4×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690721 | 2 |
| C2×#15690720 | 2 |
| C2×C8×Dic97 | 2 |
| C42×Dic97 | 2 |
| C2×#97×C97 | 2 |
| C4×#97 | 97 |