Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D97 | C2 | semidirect |
| 3. #20261030 | C2 | semidirect |
| 4. #20261026 | C2 | semidirect |
| 5. #20261022 | C2 | semidirect |
| 6. #20261018 | C2 | semidirect |
| 7. #20261014 | C2 | semidirect |
| 8. #20260776 | C2 | semidirect |
| 9. #20260757 | C2 | semidirect |
| 11. #477×C97 | C2 | semidirect |
| 44. #13095512 | Q8 | semidirect |
| 86. Q8×C97 | C2×Q8 | semidirect |
| 100. D388 | C2×Q8 | semidirect |
| 138. C97 | #3079 | semidirect |
| 142. #477 | D97 | semidirect |
| 226. Q8 | Q8×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D97 | 2 |
| C4×#13095512 | 2 |
| #20261030 | 2 |
| #20261026 | 2 |
| #20261022 | 2 |
| #20261018 | 2 |
| #20261014 | 2 |
| #20260776 | 2 |
| #20260757 | 2 |
| #20260735 | 2 |
| #477×C97 | 2 |
| #3079 | 97 |