Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 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 |
|---|---|---|
| 3. C2×#15690864 | C2 | direct (N × H) |
| 6. C2×#13095519 | C4 | semidirect |
| 8. C22×#11715897 | C4 | semidirect |
| 11. #15690864 | C22 | direct (N × H) |
| 13. C22×#11715895 | C4 | semidirect |
| 14. C2×C8×D97 | C4 | semidirect |
| 16. C22×C8×C97 | C4 | semidirect |
| 19. #13095519 | C2×C4 | semidirect |
| 21. C2×#11715897 | C2×C4 | semidirect |
| 30. C2×#11715895 | C2×C4 | semidirect |
| 31. C8×D97 | C2×C4 | semidirect |
| 34. C2×C8×C97 | C2×C4 | semidirect |
| 50. #11715897 | C22×C4 | semidirect |
| 51. C8×C97 | C22×C4 | semidirect |
| 52. #11715895 | C22×C4 | semidirect |
| 53. C22×C97 | #97 | semidirect |
| 55. C2×D97 | #97 | semidirect |
| 64. C2×C97 | C2×#97 | semidirect |
| 66. D97 | C2×#97 | semidirect |
| 69. C97 | C22×#97 | semidirect |
| 82. C22×C8 | #87604 | semidirect |
| 101. C2×C8 | C2×#87604 | semidirect |
| 121. C8 | C22×#87604 | semidirect |
| 126. C22 | #15690864 | direct (N × H) |
| 135. C2 | C2×#15690864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095519 | 2 |
| C22×C4×#87604 | 2 |
| C2×#15690864 | 2 |
| C22×C8×D97 | 2 |
| C22×#97 | 97 |