Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #41×Dic97 | C2 | semidirect |
| 3. C2×#15690736 | C2 | semidirect |
| 4. #20260708 | C2 | semidirect |
| 5. #20260506 | C2 | semidirect |
| 6. #20260494 | C2 | semidirect |
| 7. #421×C97 | C2 | semidirect |
| 10. #15690840 | C4 | semidirect |
| 12. #15690835 | C4 | semidirect |
| 33. C2×Dic194 | C2×C4 | semidirect |
| 34. C2×D388 | C2×C4 | semidirect |
| 44. #13095495 | C2×C4 | semidirect |
| 130. C97 | #1906 | semidirect |
| 133. #421 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261533 | 2 |
| #41×Dic97 | 2 |
| C2×#15690736 | 2 |
| #20260708 | 2 |
| #20260506 | 2 |
| #20260494 | 2 |
| #421×C97 | 2 |
| #1906 | 97 |