Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
166 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 58 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. #20266227 | C2 | semidirect |
| 3. #20266038 | C2 | semidirect |
| 4. #20266027 | C2 | semidirect |
| 6. C8×#11717581 | C2 | semidirect |
| 58. #11717581 | SD16 | semidirect |
| 59. C8×C101 | M16 | semidirect |
| 78. C101 | #1590 | semidirect |
| 138. C8 | #13108084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266227 | 2 |
| #20266211 | 2 |
| #20266038 | 2 |
| #20266027 | 2 |
| #20266025 | 2 |
| C8×#11717581 | 2 |
| #20265264 | 2 |
| #1590 | 101 |