Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
408 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 105 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×#13095494 | C2 | semidirect |
| 3. C2×#15690722 | C2 | semidirect |
| 4. C2×#15690722 | C2 | semidirect |
| 5. C2×#15690722 | C2 | semidirect |
| 6. #20260490 | C2 | semidirect |
| 7. #336×C97 | C2 | semidirect |
| 52. C2×#11715895 | D4 | semidirect |
| 64. C2×C8×C97 | D4 | semidirect |
| 81. C22×D97 | M16 | semidirect |
| 87. C2×C4×C97 | M16 | semidirect |
| 152. C97 | #1870 | semidirect |
| 159. #336 | D97 | semidirect |
| 213. C2×C8 | D388 | semidirect |
| 254. C2×C4 | #13095494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095494 | 2 |
| C2×C4×D388 | 2 |
| C2×#15690722 | 2 |
| #20260490 | 2 |
| #336×C97 | 2 |
| #1870 | 97 |