Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
992 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#13095520 | C2 | semidirect |
| 2. C2×#15690870 | C2 | direct (N × H) |
| 5. C2×#13095520 | C22 | semidirect |
| 7. #15690870 | C22 | direct (N × H) |
| 16. #13095520 | C23 | semidirect |
| 68. C22×C97 | #100 | semidirect |
| 81. C2×C97 | C2×#100 | semidirect |
| 85. C97 | C22×#100 | semidirect |
| 157. C22 | #15690870 | direct (N × H) |
| 167. C2 | C2×#15690870 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095520 | 2 |
| C2×#15690870 | 2 |
| C23×C22⋊D97 | 2 |
| C22×#100 | 97 |