Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#15690809 | C2 | semidirect |
| 3. #20261029 | C2 | semidirect |
| 4. #20261024 | C2 | semidirect |
| 5. #20261019 | C2 | semidirect |
| 6. #20261014 | C2 | semidirect |
| 7. #20260778 | C2 | semidirect |
| 8. #20260758 | C2 | semidirect |
| 11. #428×C97 | C2 | semidirect |
| 44. #13095511 | Q8 | semidirect |
| 104. D388 | C2×Q8 | semidirect |
| 111. Dic194 | C2×Q8 | semidirect |
| 139. C97 | #3079 | semidirect |
| 147. #428 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690809 | 2 |
| #20261203 | 2 |
| #20261029 | 2 |
| #20261024 | 2 |
| #20261019 | 2 |
| #20261014 | 2 |
| #20260778 | 2 |
| #20260758 | 2 |
| #20260737 | 2 |
| #20260734 | 2 |
| #428×C97 | 2 |
| #3079 | 97 |