Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20266181 | C2 | semidirect |
| 2. C2×#15692320 | C2 | semidirect |
| 3. C2×#15692319 | C2 | semidirect |
| 4. #20266113 | C2 | semidirect |
| 14. #15692253 | C4 | semidirect |
| 15. #15692251 | C4 | semidirect |
| 16. #15692243 | C4 | semidirect |
| 20. #124×C101 | C4 | semidirect |
| 26. C4×#87938 | D4 | semidirect |
| 95. C101 | #1963 | semidirect |
| 107. #124 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266181 | 2 |
| C2×#15692320 | 2 |
| C2×#15692319 | 2 |
| #20266113 | 2 |
| #20265726 | 2 |
| #1963 | 101 |