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. #20261031 | C2 | semidirect |
| 4. #20261027 | C2 | semidirect |
| 5. #20261025 | C2 | semidirect |
| 6. #20261019 | C2 | semidirect |
| 7. #20261013 | C2 | semidirect |
| 8. #20260774 | C2 | semidirect |
| 9. #20260757 | C2 | semidirect |
| 11. #476×C97 | C2 | semidirect |
| 44. #13095510 | Q8 | semidirect |
| 86. D4×C97 | C2×Q8 | semidirect |
| 110. Dic194 | C2×Q8 | semidirect |
| 138. C97 | #3079 | semidirect |
| 144. #476 | D97 | semidirect |
| 229. D4 | 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×#13095510 | 2 |
| #20261031 | 2 |
| #20261027 | 2 |
| #20261025 | 2 |
| #20261019 | 2 |
| #20261013 | 2 |
| #20260774 | 2 |
| #20260757 | 2 |
| #20260733 | 2 |
| #476×C97 | 2 |
| #3079 | 97 |