Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 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. #20260853 | C2 | semidirect |
| 3. #20260565 | C2 | semidirect |
| 4. #20260543 | C2 | semidirect |
| 5. C4×C16×C97 | C2 | semidirect |
| 8. Dic776 | C4 | semidirect |
| 9. #15690755 | C4 | semidirect |
| 10. D1552 | C4 | semidirect |
| 50. C97 | #2178 | semidirect |
| 55. C4×C16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261167 | 2 |
| #20260853 | 2 |
| #20260565 | 2 |
| #20260543 | 2 |
| C4×C16×C97 | 2 |
| #2178 | 97 |