Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
184 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20266041 | C2 | semidirect |
| 3. #20266040 | C2 | semidirect |
| 44. C8×C101 | M16 | semidirect |
| 46. #11717579 | M16 | semidirect |
| 64. C101 | #1567 | semidirect |
| 110. C8 | #13108083 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266180 | 2 |
| #20266041 | 2 |
| #20266040 | 2 |
| C2×C8×Dic101 | 2 |
| #1567 | 101 |