Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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×D776 | C2 | semidirect |
| 2. #20261170 | C2 | direct (N × H) |
| 3. C2×#15690753 | C2 | semidirect |
| 4. C2×#15690751 | C2 | semidirect |
| 5. C2×#15690750 | C2 | semidirect |
| 6. C2×#135×C97 | C2 | semidirect |
| 11. C2×D776 | C22 | semidirect |
| 12. #15690753 | C22 | semidirect |
| 13. #15690751 | C22 | semidirect |
| 14. #15690750 | C22 | semidirect |
| 15. C2×#13095486 | C22 | semidirect |
| 18. #135×C97 | C22 | semidirect |
| 19. C2×Q16×C97 | C22 | semidirect |
| 21. C2×D8×C97 | C22 | semidirect |
| 31. #13095486 | C23 | semidirect |
| 40. Q16×C97 | C23 | semidirect |
| 43. D8×C97 | C23 | semidirect |
| 84. C2×C97 | #509 | semidirect |
| 88. C97 | C2×#509 | semidirect |
| 89. C2×#135 | D97 | semidirect |
| 98. #135 | C2×D97 | semidirect |
| 99. C2×Q16 | C2×D97 | semidirect |
| 105. C2×D8 | C2×D97 | semidirect |
| 124. Q16 | C22×D97 | semidirect |
| 130. D8 | C22×D97 | semidirect |
| 173. C2 | #20261170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| #20261170 | 2 |
| C2×#15690753 | 2 |
| C2×#15690751 | 2 |
| C2×#15690750 | 2 |
| C2×#135×C97 | 2 |
| C2×#509 | 97 |