Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 233 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. #20265076 | C2 | semidirect |
| 3. #20265043 | C2 | semidirect |
| 5. C4⋊C4×Dic101 | C2 | semidirect |
| 7. #20265023 | C2 | semidirect |
| 21. #117×C101 | C4 | semidirect |
| 95. C101 | #2346 | semidirect |
| 105. #117 | Dic101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265076 | 2 |
| #20265070 | 2 |
| #20265043 | 2 |
| #20265037 | 2 |
| C4⋊C4×Dic101 | 2 |
| C4×C22⋊Dic101 | 2 |
| #20265023 | 2 |
| C2×#117×C101 | 2 |
| #2346 | 101 |