Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#15692254 | C2 | semidirect |
| 3. #20265465 | C2 | direct (N × H) |
| 4. C2×#15692187 | C2 | semidirect |
| 5. C2×#15692186 | C2 | semidirect |
| 6. C2×#15692184 | C2 | semidirect |
| 13. #15692254 | C22 | semidirect |
| 21. #15692187 | C22 | semidirect |
| 22. #15692186 | C22 | semidirect |
| 23. #15692184 | C22 | semidirect |
| 50. C2×D4×C101 | Q8 | semidirect |
| 65. D4×C101 | C2×Q8 | semidirect |
| 101. C2×C101 | #476 | semidirect |
| 106. C101 | C2×#476 | semidirect |
| 140. C2×D4 | Dic202 | semidirect |
| 172. D4 | C2×Dic202 | semidirect |
| 207. C2 | #20265465 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692254 | 2 |
| C2×D4×Dic101 | 2 |
| #20265465 | 2 |
| C2×#15692187 | 2 |
| C2×#15692186 | 2 |
| C2×#15692184 | 2 |
| C2×#15692176 | 2 |
| C2×#102×C101 | 2 |
| C2×#476 | 101 |