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. C22×D808 | C2 | semidirect |
| 2. C2×#15692261 | C2 | semidirect |
| 3. #20265746 | C2 | semidirect |
| 4. #20265431 | C2 | semidirect |
| 5. #20265414 | C2 | semidirect |
| 6. #20265181 | C2 | semidirect |
| 7. #427×C101 | C2 | semidirect |
| 15. C2×#13108057 | C22 | semidirect |
| 16. C2×C8×D101 | C22 | semidirect |
| 19. #15692230 | C22 | semidirect |
| 21. #15692175 | C22 | semidirect |
| 24. #107×C101 | C22 | semidirect |
| 25. #106×C101 | C22 | semidirect |
| 46. C2×C8×C101 | D4 | semidirect |
| 94. C101 | #3058 | semidirect |
| 100. #427 | D101 | semidirect |
| 117. #107 | C2×D101 | semidirect |
| 118. #106 | C2×D101 | semidirect |
| 139. C2×C8 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D808 | 2 |
| C2×#15692261 | 2 |
| #20265746 | 2 |
| #20265431 | 2 |
| #20265414 | 2 |
| #20265181 | 2 |
| #427×C101 | 2 |
| #3058 | 101 |