Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13095501 | C2 | semidirect |
| 3. #20261114 | C2 | semidirect |
| 4. #20260974 | C2 | semidirect |
| 5. #20260945 | C2 | semidirect |
| 6. #20260942 | C2 | semidirect |
| 7. #20260891 | C2 | semidirect |
| 8. #20260890 | C2 | semidirect |
| 9. C4×#13095501 | C2 | semidirect |
| 52. #13095501 | D4 | direct (N × H) |
| 88. D4×C97 | Q16 | semidirect |
| 113. C22×C97 | C2×Q16 | semidirect |
| 120. C4×C97 | C2×Q16 | semidirect |
| 131. C97 | D4×Q16 | semidirect |
| 224. D4 | #13095501 | direct (N × H) |
| 244. C22 | C2×#13095501 | semidirect |
| 254. C4 | C2×#13095501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095501 | 2 |
| D4×Dic194 | 2 |
| #20261114 | 2 |
| #20260974 | 2 |
| #20260945 | 2 |
| #20260942 | 2 |
| #20260891 | 2 |
| #20260890 | 2 |
| C4×#13095501 | 2 |
| D4×#11715895 | 2 |
| D4×Q8×C97 | 2 |
| D4×Q16 | 97 |