Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#15692183 | C2 | semidirect |
| 3. #20265179 | C2 | semidirect |
| 4. #20265178 | C2 | semidirect |
| 5. C2×#15692171 | C2 | semidirect |
| 6. #20265079 | C2 | semidirect |
| 7. C2×#104×C101 | C2 | semidirect |
| 11. #15692301 | C4 | semidirect |
| 19. C2×#13108058 | C22 | semidirect |
| 20. C2×C4⋊Dic101 | C22 | semidirect |
| 29. C2×M16×C101 | C22 | semidirect |
| 30. C2×C42×C101 | C22 | semidirect |
| 95. Q8×C101 | C22⋊C4 | semidirect |
| 99. D4×C101 | C22⋊C4 | semidirect |
| 124. D404 | C22⋊C4 | semidirect |
| 129. Dic202 | C22⋊C4 | semidirect |
| 166. C101 | #1792 | semidirect |
| 169. C2×#104 | D101 | semidirect |
| 187. C2×M16 | C2×D101 | semidirect |
| 190. C2×C42 | C2×D101 | semidirect |
| 263. Q8 | #13108051 | semidirect |
| 277. D4 | #13108051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692301 | 2 |
| C2×#15692183 | 2 |
| #20265179 | 2 |
| #20265178 | 2 |
| C2×#15692171 | 2 |
| #20265079 | 2 |
| C2×#104×C101 | 2 |
| #1792 | 101 |