Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C22×Dic388 | C2 | semidirect |
| 2. C2×Q16×D97 | C2 | semidirect |
| 4. #20261113 | C2 | semidirect |
| 5. #20260977 | C2 | semidirect |
| 6. #20260944 | C2 | semidirect |
| 7. #20260892 | C2 | semidirect |
| 8. #20260890 | C2 | semidirect |
| 9. #20260829 | C2 | semidirect |
| 11. #467×C97 | C2 | semidirect |
| 55. Dic388 | D4 | semidirect |
| 90. C22⋊D97 | Q16 | semidirect |
| 112. C22×C97 | C2×Q16 | semidirect |
| 116. C2×D97 | C2×Q16 | semidirect |
| 126. Dic97 | C2×Q16 | semidirect |
| 133. C97 | D4×Q16 | semidirect |
| 139. #467 | D97 | semidirect |
| 248. C22 | Q16×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic388 | 2 |
| C2×Q16×D97 | 2 |
| #20261398 | 2 |
| #20261113 | 2 |
| #20260977 | 2 |
| #20260944 | 2 |
| #20260892 | 2 |
| #20260890 | 2 |
| #20260829 | 2 |
| C8×C22⋊D97 | 2 |
| #467×C97 | 2 |
| D4×Q16 | 97 |