Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
280 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 87 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. Q8⋊#11715906 | C2 | direct (N × H) |
| 38. C2×Dic194 | C8 | semidirect |
| 41. Q8×D97 | C8 | semidirect |
| 45. C2×Q8×C97 | C8 | semidirect |
| 59. Q8×C97 | C2×C8 | semidirect |
| 73. Dic194 | C2×C8 | semidirect |
| 91. C2×C97 | Q8⋊C8 | semidirect |
| 93. D97 | Q8⋊C8 | semidirect |
| 97. C97 | C2×Q8⋊C8 | semidirect |
| 123. C2×Q8 | #11715906 | semidirect |
| 149. Q8 | C2×#11715906 | semidirect |
| 191. 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 |
|---|---|
| C2×C4⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| Q8⋊#11715906 | 2 |
| C2×Q8×#87604 | 2 |
| C2×Q8⋊C8 | 97 |