Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#15692288 | C2 | semidirect |
| 3. #20265748 | C2 | semidirect |
| 4. #20265658 | C2 | semidirect |
| 5. #20265398 | C2 | semidirect |
| 6. #20265391 | C2 | semidirect |
| 7. #20265386 | C2 | semidirect |
| 8. #20265381 | C2 | semidirect |
| 9. #20265205 | C2 | semidirect |
| 10. C2×#15692178 | C2 | semidirect |
| 11. #417×C101 | C2 | semidirect |
| 147. C101 | #3046 | semidirect |
| 157. #417 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692288 | 2 |
| C2×#15692275 | 2 |
| #20265748 | 2 |
| #20265658 | 2 |
| #20265398 | 2 |
| #20265391 | 2 |
| #20265386 | 2 |
| #20265381 | 2 |
| #20265205 | 2 |
| C2×#15692178 | 2 |
| #417×C101 | 2 |
| #3046 | 101 |