Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#15692165 | C2 | semidirect |
| 5. #20264932 | C2 | semidirect |
| 6. #20264931 | C2 | semidirect |
| 7. C2×C4×C8×C101 | C2 | semidirect |
| 11. C2×#13108057 | C4 | semidirect |
| 16. #15692167 | C4 | semidirect |
| 60. C2×C4×C101 | M16 | semidirect |
| 78. C8×C101 | C22⋊C4 | semidirect |
| 105. C101 | #1753 | semidirect |
| 109. C2×C4×C8 | D101 | semidirect |
| 175. C2×C4 | #13108057 | semidirect |
| 185. C8 | #13108051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108057 | 2 |
| C2×#15692167 | 2 |
| C2×#15692165 | 2 |
| C4×#13108051 | 2 |
| #20264932 | 2 |
| #20264931 | 2 |
| C2×C4×C8×C101 | 2 |
| #1753 | 101 |