Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20260486 | C2 | semidirect |
| 4. #20260481 | C2 | semidirect |
| 5. #500×C97 | C2 | semidirect |
| 43. C8×C97 | SD16 | semidirect |
| 61. C97 | #1693 | semidirect |
| 62. #500 | D97 | semidirect |
| 106. C8 | #13095498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260937 | 2 |
| #20260814 | 2 |
| #20260486 | 2 |
| #20260481 | 2 |
| #500×C97 | 2 |
| #1693 | 97 |