Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
344 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 72 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. #20261752 | C2 | semidirect |
| 2. #20261738 | C2 | semidirect |
| 3. #20261593 | C2 | semidirect |
| 6. #15690877 | C22 | semidirect |
| 7. #15690877 | C22 | semidirect |
| 101. C97 | #1545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261752 | 2 |
| #20261738 | 2 |
| #20261593 | 2 |
| C2×#15690806 | 2 |
| #1545 | 97 |