Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 2. C2×C8×#87604 | C2 | semidirect |
| 4. #20261600 | C2 | semidirect |
| 9. #15690867 | C4 | semidirect |
| 10. C22⋊#11715897 | C4 | semidirect |
| 14. C22×#11715895 | C4 | semidirect |
| 16. C2×C8×D97 | C4 | semidirect |
| 17. C2×C8×D97 | C4 | semidirect |
| 20. C22×C8×C97 | C4 | semidirect |
| 25. C22⋊#87604 | C8 | direct (N × H) |
| 55. C2×#87604 | C2×C8 | semidirect |
| 71. C8×C97 | C22⋊C4 | semidirect |
| 73. #11715895 | C22⋊C4 | semidirect |
| 76. C22×C97 | C4×C8 | semidirect |
| 81. C2×D97 | C4×C8 | semidirect |
| 98. C97 | C8×C22⋊C4 | semidirect |
| 112. C22×C8 | #87604 | semidirect |
| 171. C8 | C22⋊#87604 | direct (N × H) |
| 181. C22 | C8×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261703 | 2 |
| C2×C8×#87604 | 2 |
| C4×C22⋊#87604 | 2 |
| #20261600 | 2 |
| C22×C8×D97 | 2 |
| C8×C22⋊C4 | 97 |