Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20265982 | C2 | semidirect |
| 2. #20265618 | C2 | semidirect |
| 3. #20265612 | C2 | semidirect |
| 4. #20265607 | C2 | semidirect |
| 5. C2×#15692198 | C2 | semidirect |
| 6. #20265594 | C2 | semidirect |
| 7. #578×C101 | C2 | semidirect |
| 12. #15692201 | C22 | semidirect |
| 13. #15692199 | C22 | semidirect |
| 14. #15692198 | C22 | semidirect |
| 15. #15692198 | C22 | semidirect |
| 16. #15692196 | C22 | semidirect |
| 17. #15692195 | C22 | semidirect |
| 18. C2×#13108049 | C22 | semidirect |
| 21. #135×C101 | C22 | semidirect |
| 22. C2×Q16×C101 | C22 | semidirect |
| 75. C101 | #3416 | semidirect |
| 76. #578 | D101 | semidirect |
| 88. #135 | C2×D101 | semidirect |
| 89. C2×Q16 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265982 | 2 |
| #20265618 | 2 |
| #20265612 | 2 |
| #20265607 | 2 |
| C2×#15692198 | 2 |
| #20265594 | 2 |
| #578×C101 | 2 |
| #3416 | 101 |