Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 210 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×#15690885 | C2 | semidirect |
| 2. #20261791 | C2 | direct (N × H) |
| 3. C2×#15690884 | C2 | semidirect |
| 4. C2×#15690883 | C2 | semidirect |
| 6. #15690885 | C22 | semidirect |
| 7. #15690884 | C22 | semidirect |
| 8. #15690883 | C22 | semidirect |
| 9. C2×#13095514 | C22 | semidirect |
| 19. #13095514 | 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 | #20261791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690885 | 2 |
| #20261791 | 2 |
| C2×#15690884 | 2 |
| C2×#15690883 | 2 |
| C22×C8×D97 | 2 |
| C22×M32 | 97 |