Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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. #20265217 | C2 | semidirect |
| 4. #20265216 | C2 | semidirect |
| 5. #20265215 | C2 | semidirect |
| 6. #20265212 | C2 | semidirect |
| 7. #106×D101 | C2 | semidirect |
| 8. C2×#106×C101 | C2 | semidirect |
| 10. #15692261 | C4 | semidirect |
| 36. #13108058 | C2×C4 | semidirect |
| 37. #13108057 | C2×C4 | semidirect |
| 39. C8×D101 | C2×C4 | semidirect |
| 49. C2×C8×C101 | C2×C4 | semidirect |
| 91. C101 | #2912 | semidirect |
| 99. C2×#106 | D101 | semidirect |
| 133. C2×C8 | C4×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692261 | 2 |
| #20265658 | 2 |
| #20265217 | 2 |
| #20265216 | 2 |
| #20265215 | 2 |
| #20265212 | 2 |
| #106×D101 | 2 |
| C2×#106×C101 | 2 |
| #2912 | 101 |