Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15692253 | C2 | semidirect |
| 4. #20265380 | C2 | direct (N × H) |
| 5. C2×#15692184 | C2 | semidirect |
| 6. C2×#15692180 | C2 | semidirect |
| 7. C2×#15692179 | C2 | semidirect |
| 15. #15692253 | C22 | semidirect |
| 23. #15692184 | C22 | semidirect |
| 24. #15692180 | C22 | semidirect |
| 25. #15692179 | C22 | semidirect |
| 88. C2×Dic101 | SD16 | semidirect |
| 111. Dic101 | C2×SD16 | semidirect |
| 113. C2×C101 | #461 | semidirect |
| 118. C101 | C2×#461 | semidirect |
| 231. C2 | #20265380 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108062 | 2 |
| C2×#15692253 | 2 |
| C2×D4×Dic101 | 2 |
| #20265380 | 2 |
| C2×#15692184 | 2 |
| C2×#15692180 | 2 |
| C2×#15692179 | 2 |
| C22×SD16×C101 | 2 |
| C2×#461 | 101 |