Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#13095498 | C2 | semidirect |
| 3. C2×#15690799 | C2 | semidirect |
| 4. #20261120 | C2 | direct (N × H) |
| 5. C2×C8×Dic97 | C2 | semidirect |
| 6. C22×Q16×C97 | C2 | semidirect |
| 9. C2×#13095498 | C22 | semidirect |
| 14. #15690799 | C22 | semidirect |
| 17. C8×Dic97 | C22 | semidirect |
| 20. C2×Q16×C97 | C22 | semidirect |
| 75. C2×C97 | #495 | semidirect |
| 80. C97 | C2×#495 | semidirect |
| 81. C22×Q16 | D97 | semidirect |
| 90. C2×Q16 | C2×D97 | semidirect |
| 156. C2 | #20261120 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095498 | 2 |
| C22×D776 | 2 |
| C2×#15690799 | 2 |
| #20261120 | 2 |
| C2×C8×Dic97 | 2 |
| C22×Q16×C97 | 2 |
| C2×#495 | 97 |