Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×D808 | C2 | semidirect |
| 2. C22×#13108059 | C2 | semidirect |
| 3. C2×#15692251 | C2 | semidirect |
| 4. #20265552 | C2 | direct (N × H) |
| 5. C2×C8×Dic101 | C2 | semidirect |
| 6. C22×D8×C101 | C2 | semidirect |
| 10. C2×D808 | C22 | semidirect |
| 12. C2×#13108059 | C22 | semidirect |
| 15. #15692251 | C22 | semidirect |
| 17. C8×Dic101 | C22 | semidirect |
| 20. C2×D8×C101 | C22 | semidirect |
| 32. C2×#11717579 | D4 | semidirect |
| 43. C2×C8×C101 | D4 | semidirect |
| 60. C2×Dic101 | D8 | semidirect |
| 65. C8×C101 | C2×D4 | semidirect |
| 66. #11717579 | C2×D4 | semidirect |
| 79. Dic101 | C2×D8 | semidirect |
| 81. C2×C101 | #493 | semidirect |
| 86. C101 | C2×#493 | semidirect |
| 89. C22×D8 | D101 | semidirect |
| 101. C2×D8 | C2×D101 | semidirect |
| 127. C2×C8 | C22⋊D101 | semidirect |
| 152. C8 | C2×C22⋊D101 | semidirect |
| 168. C2 | #20265552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D808 | 2 |
| C22×#13108059 | 2 |
| C2×#15692251 | 2 |
| #20265552 | 2 |
| C2×C8×Dic101 | 2 |
| C22×D8×C101 | 2 |
| C2×#493 | 101 |