Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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. #20260833 | C2 | direct (N × H) |
| 4. C2×#15690743 | C2 | semidirect |
| 5. C2×#15690734 | C2 | semidirect |
| 7. C2×#15690721 | C2 | semidirect |
| 8. C2×C4×Q8×C97 | C2 | semidirect |
| 11. C2×#13095498 | C4 | semidirect |
| 19. #15690743 | C22 | semidirect |
| 20. #15690734 | C22 | semidirect |
| 22. #15690721 | C22 | semidirect |
| 25. C4×Q8×C97 | C22 | semidirect |
| 38. #13095498 | C2×C4 | semidirect |
| 40. C2×#11715895 | C2×C4 | semidirect |
| 48. C2×Q8×C97 | C2×C4 | semidirect |
| 68. Q8×C97 | C22×C4 | semidirect |
| 88. #11715895 | C22×C4 | semidirect |
| 105. C2×C97 | #440 | semidirect |
| 111. C97 | C2×#440 | 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 |
| 217. C2 | #20260833 | 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 |
| #20260833 | 2 |
| C2×#15690743 | 2 |
| C2×#15690734 | 2 |
| C2×#15690730 | 2 |
| C2×#15690721 | 2 |
| C2×C4×Q8×C97 | 2 |
| C2×#440 | 97 |