Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 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×#15690744 | C2 | semidirect |
| 3. #20260540 | C2 | semidirect |
| 4. #20260537 | C2 | semidirect |
| 5. C2×M32×C97 | C2 | semidirect |
| 8. #15690832 | C4 | semidirect |
| 26. Dic388 | C2×C4 | semidirect |
| 29. D776 | C2×C4 | semidirect |
| 74. C97 | #2139 | semidirect |
| 76. C2×M32 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| C2×#15690744 | 2 |
| #20260540 | 2 |
| #20260537 | 2 |
| C2×M32×C97 | 2 |
| #2139 | 97 |