Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#15690833 | C2 | semidirect |
| 2. #20261407 | C2 | semidirect |
| 3. #20261112 | C2 | semidirect |
| 4. #20260972 | C2 | semidirect |
| 5. #20260935 | C2 | semidirect |
| 6. #20260883 | C2 | semidirect |
| 7. C8×D388 | C2 | semidirect |
| 8. C4×Q16×C97 | C2 | semidirect |
| 48. Q16×C97 | D4 | semidirect |
| 88. C4×C97 | #135 | semidirect |
| 98. C97 | #3287 | semidirect |
| 105. C4×Q16 | D97 | semidirect |
| 138. Q16 | D388 | semidirect |
| 187. C4 | #15690833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| #20261407 | 2 |
| #20261112 | 2 |
| #20260972 | 2 |
| #20260935 | 2 |
| #20260883 | 2 |
| C8×D388 | 2 |
| C4×Q16×C97 | 2 |
| #3287 | 97 |