Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×#13095486 | C2 | semidirect |
| 3. #20260520 | C2 | direct (N × H) |
| 4. C2×M32×C97 | C2 | semidirect |
| 15. C2×#13095486 | C22 | semidirect |
| 18. M32×C97 | C22 | semidirect |
| 79. C2×C97 | #350 | semidirect |
| 83. C97 | C2×#350 | semidirect |
| 85. C2×M32 | D97 | semidirect |
| 98. M32 | C2×D97 | semidirect |
| 163. C2 | #20260520 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690816 | 2 |
| C22×#13095486 | 2 |
| #20260520 | 2 |
| C2×M32×C97 | 2 |
| C2×#350 | 97 |