Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 2. #20261145 | C2 | semidirect |
| 3. #20261138 | C2 | semidirect |
| 4. #20261131 | C2 | semidirect |
| 33. #13095495 | Q8 | semidirect |
| 74. #11715895 | C2×Q8 | semidirect |
| 93. C97 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690810 | 2 |
| #20261145 | 2 |
| #20261138 | 2 |
| #20261131 | 2 |
| #20260778 | 2 |
| C4×#13095495 | 2 |
| #533×C97 | 2 |
| #3165 | 97 |