Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 199 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×#15690907 | C2 | semidirect |
| 2. #20261854 | C2 | direct (N × H) |
| 3. C2×#15690906 | C2 | semidirect |
| 4. C2×#15690905 | C2 | semidirect |
| 6. #15690907 | C22 | semidirect |
| 7. #15690906 | C22 | semidirect |
| 8. #15690905 | C22 | semidirect |
| 9. C2×#13095523 | C22 | semidirect |
| 19. #13095523 | C23 | semidirect |
| 70. C2×D97 | M32 | semidirect |
| 79. C2×C97 | C2×M32 | semidirect |
| 82. D97 | C2×M32 | semidirect |
| 84. C97 | C22×M32 | semidirect |
| 165. C2 | #20261854 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690907 | 2 |
| #20261854 | 2 |
| C2×#15690906 | 2 |
| C2×#15690905 | 2 |
| C22×#13095519 | 2 |
| C22×M32 | 97 |