Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. D8×Dic97 | C2 | semidirect |
| 3. #20260817 | C2 | semidirect |
| 4. #20260562 | C2 | semidirect |
| 5. #20260537 | C2 | semidirect |
| 6. #20260510 | C2 | semidirect |
| 7. #357×C97 | C2 | semidirect |
| 11. #15690751 | C4 | semidirect |
| 24. D776 | C2×C4 | semidirect |
| 30. #13095486 | C2×C4 | semidirect |
| 33. D8×C97 | C2×C4 | semidirect |
| 72. C97 | #2177 | semidirect |
| 78. #357 | D97 | semidirect |
| 99. D8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690751 | 2 |
| D8×Dic97 | 2 |
| #20260817 | 2 |
| #20260562 | 2 |
| #20260537 | 2 |
| #20260510 | 2 |
| #357×C97 | 2 |
| #2177 | 97 |