Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 27. #13095486 | Q8 | semidirect |
| 31. C16×C97 | Q8 | semidirect |
| 56. C97 | #2255 | semidirect |
| 87. C16 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261139 | 2 |
| #20261136 | 2 |
| #20260562 | 2 |
| #20260561 | 2 |
| #20260560 | 2 |
| #20260510 | 2 |
| #367×C97 | 2 |
| #2255 | 97 |