Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
480 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 170 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. #20261775 | 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 |
| 43. Dic388 | C2×C4 | semidirect |
| 44. #13095501 | C2×C4 | semidirect |
| 49. Q16×C97 | C2×C4 | semidirect |
| 87. C2×C97 | #441 | semidirect |
| 89. D97 | #441 | semidirect |
| 92. C97 | C2×#441 | semidirect |
| 104. C2×Q16 | #87604 | semidirect |
| 129. Q16 | C2×#87604 | semidirect |
| 181. C2 | #20261775 | 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 |
| #20261775 | 2 |
| C2×#15690878 | 2 |
| C2×#15690873 | 2 |
| C2×#15690864 | 2 |
| C2×Q16×D97 | 2 |
| C2×#441 | 97 |