Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. #20261151 | C2 | semidirect |
| 2. #20261002 | C2 | semidirect |
| 3. #20260565 | C2 | semidirect |
| 4. #20260548 | C2 | semidirect |
| 5. C2×D16×C97 | C2 | semidirect |
| 55. C97 | #2221 | semidirect |
| 56. C2×D16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261151 | 2 |
| #20261002 | 2 |
| #20260565 | 2 |
| #20260548 | 2 |
| C2×D16×C97 | 2 |
| #2221 | 97 |