Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C4×#13095498 | C2 | direct (N × H) |
| 4. C2×#15690741 | C2 | semidirect |
| 5. C2×#15690734 | C2 | semidirect |
| 7. C2×C4×#11715895 | C2 | semidirect |
| 8. C2×C4×Q8×C97 | C2 | semidirect |
| 11. C2×#13095498 | C4 | direct (N × H) |
| 19. #15690741 | C22 | semidirect |
| 20. #15690734 | C22 | semidirect |
| 22. C4×#11715895 | C22 | semidirect |
| 25. C4×Q8×C97 | C22 | semidirect |
| 38. #13095498 | C2×C4 | direct (N × H) |
| 40. C2×#11715895 | C2×C4 | semidirect |
| 48. C2×Q8×C97 | C2×C4 | semidirect |
| 68. Q8×C97 | C22×C4 | semidirect |
| 74. C2×C4×C97 | SD16 | semidirect |
| 88. #11715895 | C22×C4 | semidirect |
| 101. C4×C97 | C2×SD16 | semidirect |
| 105. C2×C97 | C4×SD16 | semidirect |
| 111. C97 | C2×C4×SD16 | semidirect |
| 113. C2×C4×Q8 | D97 | semidirect |
| 128. C4×Q8 | C2×D97 | semidirect |
| 144. C2×Q8 | C4×D97 | semidirect |
| 179. Q8 | C2×C4×D97 | semidirect |
| 191. C2×C4 | #13095498 | direct (N × H) |
| 213. C4 | C2×#13095498 | direct (N × H) |
| 217. C2 | C4×#13095498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095498 | 2 |
| C2×C4×D388 | 2 |
| C4×#13095498 | 2 |
| C2×#15690741 | 2 |
| C2×#15690734 | 2 |
| C2×#15690730 | 2 |
| C2×C4×#11715895 | 2 |
| C2×C4×Q8×C97 | 2 |
| C2×C4×SD16 | 97 |