Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
578 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20261210 | C2 | semidirect |
| 3. #20260590 | C2 | semidirect |
| 4. #20260501 | C2 | semidirect |
| 5. C2×#99×C97 | C2 | semidirect |
| 9. #15690778 | C4 | semidirect |
| 25. C23×D97 | C2×C4 | semidirect |
| 30. C22×Dic97 | D4 | semidirect |
| 36. C22⋊Dic97 | C2×C4 | semidirect |
| 54. C23×C97 | C22⋊C4 | semidirect |
| 78. C2×C4×C97 | C22⋊C4 | semidirect |
| 120. C97 | #1889 | semidirect |
| 123. C2×#99 | D97 | semidirect |
| 186. C23 | #13095488 | semidirect |
| 204. C2×C4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690778 | 2 |
| #20261210 | 2 |
| #20260590 | 2 |
| #20260501 | 2 |
| C2×#99×C97 | 2 |
| #1889 | 97 |