Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 50 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. Q16×#87604 | C2 | semidirect |
| 3. #20261662 | C2 | semidirect |
| 4. #20261648 | C2 | semidirect |
| 6. C16×#87604 | C2 | semidirect |
| 18. #15690755 | C4 | semidirect |
| 19. #15690754 | C4 | semidirect |
| 20. #15690753 | C4 | semidirect |
| 22. SD32×C97 | C4 | semidirect |
| 34. Dic388 | C2×C4 | semidirect |
| 39. #13095486 | C2×C4 | semidirect |
| 40. Q16×C97 | C2×C4 | semidirect |
| 42. C16×C97 | C2×C4 | semidirect |
| 68. #87604 | SD32 | direct (N × H) |
| 79. C97 | C4×SD32 | semidirect |
| 94. SD32 | #87604 | direct (N × H) |
| 107. Q16 | C2×#87604 | semidirect |
| 121. C16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#87604 | 2 |
| D8×#87604 | 2 |
| #20261662 | 2 |
| #20261648 | 2 |
| #20261647 | 2 |
| C16×#87604 | 2 |
| SD32×D97 | 2 |
| C4×SD32 | 97 |