Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
696 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 177 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×#15692244 | C2 | semidirect |
| 3. C22×C4×Dic101 | C2 | semidirect |
| 4. #20265084 | C2 | semidirect |
| 5. #20265078 | C2 | semidirect |
| 6. #20265067 | C2 | semidirect |
| 7. #20265054 | C2 | semidirect |
| 8. #20265042 | C2 | semidirect |
| 9. C2×C22⋊Q8×C101 | C2 | semidirect |
| 49. C4×Dic101 | D4 | semidirect |
| 103. C22×C101 | #124 | semidirect |
| 129. C101 | #2850 | semidirect |
| 131. C2×C22⋊Q8 | D101 | semidirect |
| 237. C22 | #15692244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692244 | 2 |
| C2×#15692229 | 2 |
| C22×C4×Dic101 | 2 |
| #20265084 | 2 |
| #20265078 | 2 |
| #20265067 | 2 |
| #20265054 | 2 |
| #20265042 | 2 |
| C2×C22⋊Q8×C101 | 2 |
| #2850 | 101 |