Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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. #20261641 | C2 | direct (N × H) |
| 9. #15690799 | C4 | semidirect |
| 12. C2×C4×Dic97 | C4 | semidirect |
| 13. C22×Q8×C97 | C4 | semidirect |
| 27. C4×Dic97 | C2×C4 | semidirect |
| 31. C2×Q8×C97 | C2×C4 | semidirect |
| 73. C2×C97 | #354 | semidirect |
| 78. C97 | C2×#354 | semidirect |
| 82. C22×Q8 | #87604 | semidirect |
| 96. C2×Q8 | C2×#87604 | semidirect |
| 153. C2 | #20261641 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690869 | 2 |
| #20261641 | 2 |
| C2×#15690799 | 2 |
| C2×#354 | 97 |