Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#15690746 | C2 | semidirect |
| 3. #20260549 | C2 | direct (N × H) |
| 4. C2×M32×C97 | C2 | semidirect |
| 14. #15690746 | C22 | semidirect |
| 17. M32×C97 | C22 | semidirect |
| 75. C2×C97 | #361 | semidirect |
| 79. C97 | C2×#361 | semidirect |
| 81. C2×M32 | D97 | semidirect |
| 94. M32 | C2×D97 | semidirect |
| 155. C2 | #20260549 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C2×#15690746 | 2 |
| #20260549 | 2 |
| C2×M32×C97 | 2 |
| C2×#361 | 97 |