Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C2×#15692180 | C2 | semidirect |
| 4. C2×#15692178 | C2 | semidirect |
| 6. #20264939 | C2 | semidirect |
| 7. #340×C101 | C2 | semidirect |
| 13. #15692235 | C4 | semidirect |
| 32. C2×Dic202 | C2×C4 | semidirect |
| 61. C4⋊C4×C101 | C2×C4 | semidirect |
| 116. C2×D101 | #103 | semidirect |
| 135. C101 | #1872 | semidirect |
| 142. #340 | D101 | semidirect |
| 195. C4⋊C4 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692235 | 2 |
| C2×C4⋊C4×D101 | 2 |
| C2×#15692180 | 2 |
| C2×#15692178 | 2 |
| C2×#15692167 | 2 |
| #20264939 | 2 |
| #340×C101 | 2 |
| #1872 | 101 |