Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1664 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 850 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. C2×Q8×#87604 | C2 | direct (N × H) |
| 7. Q8×#87604 | C22 | direct (N × H) |
| 10. C22×Dic194 | C4 | semidirect |
| 11. C2×Q8×D97 | C4 | semidirect |
| 14. C22×Q8×C97 | C4 | semidirect |
| 16. C22×#87604 | Q8 | direct (N × H) |
| 22. C2×Dic194 | C2×C4 | semidirect |
| 23. Q8×D97 | C2×C4 | semidirect |
| 28. C2×Q8×C97 | C2×C4 | semidirect |
| 36. C2×#87604 | C2×Q8 | direct (N × H) |
| 39. Q8×C97 | C22×C4 | semidirect |
| 44. Dic194 | C22×C4 | semidirect |
| 45. C22×C97 | C4×Q8 | semidirect |
| 47. C2×D97 | C4×Q8 | semidirect |
| 53. #87604 | C22×Q8 | direct (N × H) |
| 56. C2×C97 | C2×C4×Q8 | semidirect |
| 58. D97 | C2×C4×Q8 | semidirect |
| 62. C97 | C22×C4×Q8 | semidirect |
| 70. C22×Q8 | #87604 | direct (N × H) |
| 81. C2×Q8 | C2×#87604 | direct (N × H) |
| 98. Q8 | C22×#87604 | direct (N × H) |
| 112. C22 | Q8×#87604 | direct (N × H) |
| 121. C2 | C2×Q8×#87604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#87604 | 2 |
| C22×C4⋊#87604 | 2 |
| C22×C4×#87604 | 2 |
| C22×Q8×D97 | 2 |
| C22×C4×Q8 | 97 |