Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20261027 | C2 | semidirect |
| 3. #20261022 | C2 | semidirect |
| 4. #20261017 | C2 | semidirect |
| 5. #20261012 | C2 | semidirect |
| 6. #20260775 | C2 | semidirect |
| 7. #20260759 | C2 | semidirect |
| 9. C2×C4⋊Q8×C97 | C2 | semidirect |
| 36. #13095511 | Q8 | semidirect |
| 91. D388 | C2×Q8 | semidirect |
| 96. Dic194 | C2×Q8 | semidirect |
| 122. C97 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095511 | 2 |
| #20261027 | 2 |
| #20261022 | 2 |
| #20261017 | 2 |
| #20261012 | 2 |
| #20260775 | 2 |
| #20260759 | 2 |
| #20260734 | 2 |
| C2×C4⋊Q8×C97 | 2 |
| #3079 | 97 |