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×#15692180 | C2 | semidirect |
| 3. C2×#15692178 | C2 | semidirect |
| 4. C2×#15692176 | C2 | semidirect |
| 5. C2×#15692167 | C2 | semidirect |
| 6. #20265034 | C2 | semidirect |
| 7. C2×#102×C101 | C2 | semidirect |
| 13. C2×#13108073 | C4 | semidirect |
| 94. D4×C101 | C22⋊C4 | semidirect |
| 122. Dic202 | C22⋊C4 | semidirect |
| 164. C101 | #1788 | semidirect |
| 169. C2×#102 | D101 | semidirect |
| 263. D4 | #13108051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108073 | 2 |
| C2×#15692180 | 2 |
| C2×#15692178 | 2 |
| C2×#15692176 | 2 |
| C2×#15692167 | 2 |
| #20265034 | 2 |
| C2×#102×C101 | 2 |
| #1788 | 101 |