Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 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. #20261007 | C2 | semidirect |
| 4. #20260565 | C2 | semidirect |
| 5. #20260551 | C2 | semidirect |
| 6. #20260548 | C2 | semidirect |
| 7. C2×SD32×C97 | C2 | semidirect |
| 72. C97 | #2223 | semidirect |
| 73. C2×SD32 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261151 | 2 |
| #20261007 | 2 |
| #20261002 | 2 |
| #20260565 | 2 |
| #20260551 | 2 |
| #20260548 | 2 |
| C2×SD32×C97 | 2 |
| #2223 | 97 |