Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20265978 | C2 | semidirect |
| 2. #20265444 | C2 | semidirect |
| 3. #20265344 | C2 | semidirect |
| 4. #20265295 | C2 | semidirect |
| 5. #493×C101 | C2 | semidirect |
| 6. #15692300 | C22 | semidirect |
| 7. #15692281 | C22 | semidirect |
| 12. #15692261 | C22 | semidirect |
| 13. #15692191 | C22 | semidirect |
| 14. #15692183 | C22 | semidirect |
| 15. #15692172 | C22 | semidirect |
| 16. C2×D8×C101 | C22 | semidirect |
| 17. #127×C101 | C22 | semidirect |
| 18. C4×C8×C101 | C22 | semidirect |
| 23. Dic404 | D4 | semidirect |
| 24. #13108063 | D4 | semidirect |
| 26. D808 | D4 | semidirect |
| 65. C101 | #3292 | semidirect |
| 67. #493 | D101 | semidirect |
| 77. C2×D8 | C2×D101 | semidirect |
| 79. #127 | C2×D101 | semidirect |
| 83. C4×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265978 | 2 |
| #20265444 | 2 |
| #20265344 | 2 |
| #20265295 | 2 |
| #493×C101 | 2 |
| #3292 | 101 |