Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20265976 | C2 | semidirect |
| 2. C2×#15692278 | C2 | semidirect |
| 3. #131×D101 | C2 | semidirect |
| 4. #20265449 | C2 | semidirect |
| 5. #20265448 | C2 | semidirect |
| 6. #20265447 | C2 | semidirect |
| 7. #20265443 | C2 | semidirect |
| 8. #20265442 | C2 | semidirect |
| 9. #108×D101 | C2 | semidirect |
| 10. #20265160 | C2 | semidirect |
| 11. #473×C101 | C2 | semidirect |
| 25. C2×#13108061 | C22 | semidirect |
| 26. C2×D808 | C22 | semidirect |
| 37. #15692191 | C22 | semidirect |
| 38. #15692190 | C22 | semidirect |
| 39. #15692174 | C22 | semidirect |
| 40. #15692171 | C22 | semidirect |
| 41. #15692171 | C22 | semidirect |
| 43. C2×Q16×C101 | C22 | semidirect |
| 45. #108×C101 | C22 | semidirect |
| 46. #101×C101 | C22 | semidirect |
| 167. C101 | #3067 | semidirect |
| 172. #473 | D101 | semidirect |
| 193. C2×Q16 | C2×D101 | semidirect |
| 209. #108 | C2×D101 | semidirect |
| 211. #101 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265976 | 2 |
| C2×#15692278 | 2 |
| #131×D101 | 2 |
| #20265449 | 2 |
| #20265448 | 2 |
| #20265447 | 2 |
| #20265443 | 2 |
| #20265442 | 2 |
| #108×D101 | 2 |
| #20265160 | 2 |
| #473×C101 | 2 |
| #3067 | 101 |