Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20265734 | C2 | semidirect |
| 3. #20265542 | C2 | semidirect |
| 4. #20265524 | C2 | semidirect |
| 5. #20265183 | C2 | semidirect |
| 6. C4×M16×C101 | C2 | semidirect |
| 9. #15692255 | C22 | semidirect |
| 13. #15692247 | C22 | semidirect |
| 17. #15692177 | C22 | semidirect |
| 20. #97×C101 | C22 | semidirect |
| 21. C4×C8×C101 | C22 | semidirect |
| 75. C101 | #3138 | semidirect |
| 81. C4×M16 | D101 | semidirect |
| 95. #97 | C2×D101 | semidirect |
| 96. C4×C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265734 | 2 |
| C2×#15692252 | 2 |
| #20265542 | 2 |
| #20265524 | 2 |
| #20265183 | 2 |
| C4×M16×C101 | 2 |
| #3138 | 101 |