Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. C2×#15692179 | C2 | semidirect |
| 3. C2×#15692177 | C2 | semidirect |
| 4. C2×#15692175 | C2 | semidirect |
| 5. C2×#15692167 | C2 | semidirect |
| 6. #20265034 | C2 | semidirect |
| 7. C2×#103×C101 | C2 | semidirect |
| 13. C2×#13108075 | C4 | semidirect |
| 94. Q8×C101 | C22⋊C4 | semidirect |
| 117. D404 | C22⋊C4 | semidirect |
| 164. C101 | #1788 | semidirect |
| 167. C2×#103 | D101 | semidirect |
| 258. Q8 | #13108051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108075 | 2 |
| C2×#15692179 | 2 |
| C2×#15692177 | 2 |
| C2×#15692175 | 2 |
| C2×#15692167 | 2 |
| #20265034 | 2 |
| C2×#103×C101 | 2 |
| #1788 | 101 |