Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
|---|---|---|
| 2. Q16×#87604 | C2 | direct (N × H) |
| 18. C2×Dic388 | C4 | semidirect |
| 19. C2×#13095501 | C4 | semidirect |
| 20. Q16×D97 | C4 | semidirect |
| 23. C2×Q16×C97 | C4 | semidirect |
| 44. Dic388 | C2×C4 | semidirect |
| 45. #13095501 | C2×C4 | semidirect |
| 50. Q16×C97 | C2×C4 | semidirect |
| 56. C2×#87604 | Q16 | direct (N × H) |
| 85. #87604 | C2×Q16 | direct (N × H) |
| 92. C2×C97 | C4×Q16 | semidirect |
| 94. D97 | C4×Q16 | semidirect |
| 98. C97 | C2×C4×Q16 | semidirect |
| 110. C2×Q16 | #87604 | direct (N × H) |
| 136. Q16 | C2×#87604 | direct (N × H) |
| 193. C2 | Q16×#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 |
| Q16×#87604 | 2 |
| C2×#15690879 | 2 |
| C2×#15690873 | 2 |
| C2×C8×#87604 | 2 |
| C2×Q16×D97 | 2 |
| C2×C4×Q16 | 97 |