Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 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×#15692247 | C2 | semidirect |
| 3. #20265532 | C2 | direct (N × H) |
| 4. C2×#15692180 | C2 | semidirect |
| 6. C2×C4×C8×C101 | C2 | semidirect |
| 10. #15692247 | C22 | semidirect |
| 16. #15692180 | C22 | semidirect |
| 20. C4×C8×C101 | C22 | semidirect |
| 69. C2×C101 | #488 | semidirect |
| 74. C101 | C2×#488 | semidirect |
| 80. C2×C4×C8 | D101 | semidirect |
| 94. C4×C8 | C2×D101 | semidirect |
| 144. C2 | #20265532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692247 | 2 |
| C2×#15692243 | 2 |
| #20265532 | 2 |
| C2×#15692180 | 2 |
| C2×#15692177 | 2 |
| C2×C4×C8×C101 | 2 |
| C2×#488 | 101 |