Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#15692261 | C2 | semidirect |
| 2. #20265744 | C2 | semidirect |
| 3. #20265427 | C2 | semidirect |
| 4. #20265410 | C2 | semidirect |
| 5. #20265215 | C2 | semidirect |
| 6. #20265182 | C2 | semidirect |
| 7. C22×D8×C101 | C2 | semidirect |
| 11. C2×#13108057 | C22 | semidirect |
| 12. C2×C8×D101 | C22 | semidirect |
| 15. #15692226 | C22 | semidirect |
| 18. #15692189 | C22 | semidirect |
| 19. #15692187 | C22 | semidirect |
| 20. #15692176 | C22 | semidirect |
| 49. C2×C8×C101 | D4 | semidirect |
| 94. C101 | #3058 | semidirect |
| 95. C22×D8 | D101 | semidirect |
| 139. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692261 | 2 |
| #20265744 | 2 |
| #20265427 | 2 |
| #20265410 | 2 |
| #20265215 | 2 |
| #20265182 | 2 |
| C22×D8×C101 | 2 |
| #3058 | 101 |