Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 15. #97×C97 | C4 | semidirect |
| 16. C4×C8×C97 | C4 | semidirect |
| 66. C97 | #1833 | semidirect |
| 81. #97 | Dic97 | semidirect |
| 82. C4×C8 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690746 | 2 |
| #20260773 | 2 |
| #20260506 | 2 |
| #20260491 | 2 |
| #405×C97 | 2 |
| #1833 | 97 |