Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×#15690775 | C2 | semidirect |
| 4. #20260834 | C2 | direct (N × H) |
| 5. C2×#15690733 | C2 | semidirect |
| 7. C2×#15690720 | C2 | semidirect |
| 8. C2×#107×C97 | C2 | semidirect |
| 12. C2×#13095500 | C4 | semidirect |
| 16. #15690775 | C22 | semidirect |
| 23. #15690733 | C22 | semidirect |
| 25. #15690720 | C22 | semidirect |
| 29. #107×C97 | C22 | semidirect |
| 33. C2×Dic194 | C2×C4 | semidirect |
| 44. #13095500 | C2×C4 | semidirect |
| 55. C2×C8×C97 | C2×C4 | semidirect |
| 86. Dic194 | C22×C4 | semidirect |
| 87. C8×C97 | C22×C4 | semidirect |
| 105. C2×C97 | #440 | semidirect |
| 111. C97 | C2×#440 | semidirect |
| 116. C2×#107 | D97 | semidirect |
| 137. #107 | C2×D97 | semidirect |
| 161. C2×C8 | C4×D97 | semidirect |
| 199. C8 | C2×C4×D97 | semidirect |
| 217. C2 | #20260834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C2×#15690775 | 2 |
| C2×#15690772 | 2 |
| #20260834 | 2 |
| C2×#15690733 | 2 |
| C2×#15690730 | 2 |
| C2×#15690720 | 2 |
| C2×#107×C97 | 2 |
| C2×#440 | 97 |