Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1102 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 213 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×#15692238 | C2 | semidirect |
| 3. #20265056 | C2 | semidirect |
| 4. #20265050 | C2 | semidirect |
| 5. #20265040 | C2 | semidirect |
| 6. #20265033 | C2 | semidirect |
| 7. C24×C4×C101 | C2 | semidirect |
| 12. C2×#13108053 | C22 | semidirect |
| 17. C2×#13108051 | C22 | semidirect |
| 18. #15692162 | C22 | semidirect |
| 48. C22×C4×C101 | D4 | semidirect |
| 84. C22×C101 | #123 | semidirect |
| 102. C101 | #2849 | semidirect |
| 103. C24×C4 | D101 | semidirect |
| 144. C22×C4 | C22⋊D101 | semidirect |
| 189. C22 | #15692238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692238 | 2 |
| C2×#15692224 | 2 |
| #20265056 | 2 |
| #20265050 | 2 |
| #20265040 | 2 |
| #20265033 | 2 |
| C24×C4×C101 | 2 |
| #2849 | 101 |