Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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×#13095494 | C2 | semidirect |
| 3. C2×C4⋊C4×D97 | C2 | semidirect |
| 4. #20260733 | C2 | direct (N × H) |
| 5. C2×#15690735 | C2 | semidirect |
| 6. C2×#15690733 | C2 | semidirect |
| 7. C2×#15690731 | C2 | semidirect |
| 8. C2×#102×C97 | C2 | semidirect |
| 11. C2×#13095510 | C4 | semidirect |
| 19. C2×#13095494 | C22 | semidirect |
| 24. C4⋊C4×D97 | C22 | semidirect |
| 25. #15690735 | C22 | semidirect |
| 26. #15690733 | C22 | semidirect |
| 27. #15690731 | C22 | semidirect |
| 31. #102×C97 | C22 | semidirect |
| 35. #13095510 | C2×C4 | semidirect |
| 38. C2×Dic194 | C2×C4 | semidirect |
| 62. C2×D4×C97 | C2×C4 | semidirect |
| 81. D4×C97 | C22×C4 | semidirect |
| 102. Dic194 | C22×C4 | semidirect |
| 125. C2×C97 | #417 | semidirect |
| 131. C97 | C2×#417 | semidirect |
| 139. C2×#102 | D97 | semidirect |
| 162. #102 | C2×D97 | semidirect |
| 176. C2×D4 | C4×D97 | semidirect |
| 216. D4 | C2×C4×D97 | semidirect |
| 257. C2 | #20260733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095510 | 2 |
| C22×#13095494 | 2 |
| C2×C4⋊C4×D97 | 2 |
| #20260733 | 2 |
| C2×#15690735 | 2 |
| C2×#15690733 | 2 |
| C2×#15690731 | 2 |
| C2×#102×C97 | 2 |
| C2×#417 | 97 |