Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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×#15692253 | C2 | semidirect |
| 4. #20265084 | C2 | semidirect |
| 5. #20265082 | C2 | semidirect |
| 6. #20265072 | C2 | semidirect |
| 7. #20265046 | C2 | semidirect |
| 36. C22×Dic101 | Q8 | semidirect |
| 99. C22×C101 | C4⋊Q8 | semidirect |
| 112. Dic101 | C22⋊Q8 | semidirect |
| 120. C101 | #2857 | semidirect |
| 219. C22 | #15692253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692253 | 2 |
| C2×#15692234 | 2 |
| C22×C4×Dic101 | 2 |
| #20265084 | 2 |
| #20265082 | 2 |
| #20265072 | 2 |
| #20265046 | 2 |
| #20265035 | 2 |
| C2×C22⋊Q8×C101 | 2 |
| #2857 | 101 |