Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
364 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 1. #20261786 | C2 | semidirect |
| 2. #20261785 | C2 | semidirect |
| 3. #20261784 | C2 | semidirect |
| 4. Q8×#11715897 | C2 | semidirect |
| 34. #13095519 | Q8 | semidirect |
| 95. C97 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261786 | 2 |
| #20261785 | 2 |
| #20261784 | 2 |
| Q8×#11715897 | 2 |
| #20261742 | 2 |
| #20261739 | 2 |
| #20261700 | 2 |
| C4×#13095519 | 2 |
| #20261290 | 2 |
| #2960 | 97 |