Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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. #20260789 | C2 | semidirect |
| 3. #20260785 | C2 | semidirect |
| 4. #20260758 | C2 | semidirect |
| 6. M16×Dic97 | C2 | semidirect |
| 17. #15690739 | C22 | semidirect |
| 19. #15690720 | C22 | semidirect |
| 20. C8×Dic97 | C22 | semidirect |
| 67. C2×Dic97 | M16 | semidirect |
| 93. C97 | #2920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic97 | 2 |
| #20260789 | 2 |
| #20260785 | 2 |
| #20260758 | 2 |
| #20260699 | 2 |
| M16×Dic97 | 2 |
| #407×C97 | 2 |
| #2920 | 97 |