Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
436 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 136 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×C8×#87604 | C2 | semidirect |
| 4. #20261600 | C2 | semidirect |
| 12. #15690867 | C4 | semidirect |
| 13. C22⋊#11715897 | C4 | semidirect |
| 17. C22⋊#11715895 | C4 | semidirect |
| 18. #15690722 | C4 | semidirect |
| 19. C22⋊C8×C97 | C4 | semidirect |
| 22. C22×#87604 | C8 | semidirect |
| 27. C2×#11715897 | C2×C4 | semidirect |
| 39. C2×#11715895 | C2×C4 | semidirect |
| 43. C2×C8×C97 | C2×C4 | semidirect |
| 75. C22×C97 | C4×C8 | semidirect |
| 81. C2×D97 | C4×C8 | semidirect |
| 87. #87604 | C22⋊C8 | direct (N × H) |
| 100. C97 | C4×C22⋊C8 | semidirect |
| 118. C22⋊C8 | #87604 | direct (N × H) |
| 140. C2×C8 | C2×#87604 | semidirect |
| 184. C22 | C8×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#87604 | 2 |
| #20261703 | 2 |
| C2×C8×#87604 | 2 |
| #20261600 | 2 |
| C22⋊C8×D97 | 2 |
| C4×C22⋊C8 | 97 |