Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 2. C2×D4×Dic101 | C2 | semidirect |
| 3. C2×#15692217 | C2 | semidirect |
| 4. C2×#15692215 | C2 | semidirect |
| 5. #20265079 | C2 | semidirect |
| 6. #20265077 | C2 | semidirect |
| 7. #20265046 | C2 | semidirect |
| 8. C42×Dic101 | C2 | semidirect |
| 9. #390×C101 | C2 | semidirect |
| 14. #15692251 | C4 | semidirect |
| 34. C2×D404 | C2×C4 | semidirect |
| 37. C2×C22⋊D101 | C2×C4 | semidirect |
| 52. C4×Dic101 | C2×C4 | semidirect |
| 53. C4×Dic101 | D4 | semidirect |
| 54. C4×Dic101 | D4 | semidirect |
| 58. C2×D4×C101 | C2×C4 | semidirect |
| 115. C4×C101 | C4×D4 | semidirect |
| 118. Dic101 | C4×D4 | semidirect |
| 119. Dic101 | #127 | semidirect |
| 128. C101 | C4×#127 | semidirect |
| 135. #390 | D101 | semidirect |
| 169. C2×D4 | C4×D101 | semidirect |
| 247. C4 | #15692215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692251 | 2 |
| C2×D4×Dic101 | 2 |
| C2×#15692217 | 2 |
| C2×#15692215 | 2 |
| #20265079 | 2 |
| #20265077 | 2 |
| #20265046 | 2 |
| C42×Dic101 | 2 |
| #390×C101 | 2 |
| C4×#127 | 101 |