Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692302 | C2 | semidirect |
| 2. C2×#15692283 | C2 | semidirect |
| 3. C2×#15692280 | C2 | semidirect |
| 4. C2×#15692243 | C2 | semidirect |
| 5. #20265351 | C2 | direct (N × H) |
| 6. C2×#15692183 | C2 | semidirect |
| 7. C2×#15692173 | C2 | semidirect |
| 8. C2×#104×C101 | C2 | semidirect |
| 12. #15692302 | C22 | semidirect |
| 22. #15692283 | C22 | semidirect |
| 24. #15692280 | C22 | semidirect |
| 31. #15692243 | C22 | semidirect |
| 33. #15692183 | C22 | semidirect |
| 34. #15692173 | C22 | semidirect |
| 38. #104×C101 | C22 | semidirect |
| 171. C2×C101 | #454 | semidirect |
| 176. C101 | C2×#454 | semidirect |
| 183. C2×#104 | D101 | semidirect |
| 213. #104 | C2×D101 | semidirect |
| 349. C2 | #20265351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| C2×#15692283 | 2 |
| C2×#15692280 | 2 |
| C2×#15692243 | 2 |
| #20265351 | 2 |
| C2×#15692183 | 2 |
| C2×#15692173 | 2 |
| C2×#104×C101 | 2 |
| C2×#454 | 101 |