Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #20266257 | C2 | semidirect |
| 2. #20266223 | C2 | semidirect |
| 3. #20266221 | C2 | semidirect |
| 4. D101⋊#108 | C2 | semidirect |
| 5. #20266176 | C2 | semidirect |
| 6. #20266140 | C2 | semidirect |
| 9. #15692343 | C22 | semidirect |
| 14. #15692326 | C22 | semidirect |
| 15. #15692325 | C22 | semidirect |
| 16. #15692320 | C22 | semidirect |
| 17. #15692309 | C22 | semidirect |
| 18. C8×#87938 | C22 | semidirect |
| 20. #15692278 | C4 | semidirect |
| 21. #15692278 | C4 | semidirect |
| 24. C2×#13108061 | C4 | semidirect |
| 25. C2×D808 | C4 | semidirect |
| 27. C2×Q16×C101 | C4 | semidirect |
| 102. C101 | #2957 | semidirect |
| 115. C2×Q16 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266257 | 2 |
| #20266223 | 2 |
| #20266221 | 2 |
| D101⋊#108 | 2 |
| #20266176 | 2 |
| #20266140 | 2 |
| C2×#15692278 | 2 |
| #2957 | 101 |