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 |
|---|---|---|
| 3. #20260488 | C2 | semidirect |
| 4. #20260481 | C2 | semidirect |
| 5. #500×C97 | C2 | semidirect |
| 44. C8×C97 | SD16 | semidirect |
| 63. C97 | #1673 | semidirect |
| 64. #500 | D97 | semidirect |
| 109. C8 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260937 | 2 |
| C8×D388 | 2 |
| #20260488 | 2 |
| #20260481 | 2 |
| #500×C97 | 2 |
| #1673 | 97 |