Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 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. #20265722 | C2 | semidirect |
| 2. C2×D4×Dic101 | C2 | semidirect |
| 3. #20265491 | C2 | semidirect |
| 4. #20265488 | C2 | semidirect |
| 5. #20265455 | C2 | semidirect |
| 6. #20265370 | C2 | semidirect |
| 7. #20265311 | C2 | semidirect |
| 8. D8×Dic101 | C2 | semidirect |
| 9. #20265257 | C2 | semidirect |
| 10. #20265227 | C2 | semidirect |
| 11. #447×C101 | C2 | semidirect |
| 15. #15692254 | C22 | semidirect |
| 16. #15692251 | C22 | semidirect |
| 24. D4×Dic101 | C22 | semidirect |
| 25. #15692217 | C22 | semidirect |
| 30. #15692189 | C22 | semidirect |
| 31. #15692188 | C22 | semidirect |
| 32. #15692184 | C22 | semidirect |
| 33. #15692177 | C22 | semidirect |
| 35. #15692176 | C22 | semidirect |
| 37. C8×Dic101 | C22 | semidirect |
| 94. D4×C101 | #41 | semidirect |
| 109. C2×Dic101 | D8 | semidirect |
| 150. C101 | #3100 | semidirect |
| 158. #447 | D101 | semidirect |
| 249. D4 | #13108073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265722 | 2 |
| C2×D4×Dic101 | 2 |
| #20265491 | 2 |
| #20265488 | 2 |
| #20265455 | 2 |
| #20265370 | 2 |
| #20265311 | 2 |
| D8×Dic101 | 2 |
| #20265257 | 2 |
| #20265227 | 2 |
| #447×C101 | 2 |
| #3100 | 101 |