Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 215 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. Q8×#11715906 | C2 | direct (N × H) |
| 15. C2×#11715906 | Q8 | direct (N × H) |
| 23. C2×Dic194 | C8 | semidirect |
| 24. Q8×D97 | C8 | semidirect |
| 27. C2×Q8×C97 | C8 | semidirect |
| 36. #11715906 | C2×Q8 | direct (N × H) |
| 37. Q8×C97 | C2×C8 | semidirect |
| 42. Dic194 | C2×C8 | semidirect |
| 54. C2×C97 | C8×Q8 | semidirect |
| 56. D97 | C8×Q8 | semidirect |
| 60. C97 | C2×C8×Q8 | semidirect |
| 77. C2×Q8 | #11715906 | direct (N × H) |
| 90. Q8 | C2×#11715906 | direct (N × H) |
| 117. C2 | Q8×#11715906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715906 | 2 |
| C2×C4⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| C2×Q8×#87604 | 2 |
| C2×C8×Q8 | 97 |