Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
146 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 53. C8×C97 | Q16 | semidirect |
| 71. C97 | #1692 | semidirect |
| 127. C8 | #13095501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261027 | 2 |
| #20260942 | 2 |
| #20260865 | 2 |
| #20260488 | 2 |
| #20260484 | 2 |
| #20260481 | 2 |
| #498×C97 | 2 |
| #1692 | 97 |