Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 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. #20265256 | C2 | semidirect |
| 3. #20265254 | C2 | semidirect |
| 4. #20265230 | C2 | semidirect |
| 5. #20265139 | C2 | semidirect |
| 6. #431×C101 | C2 | semidirect |
| 9. C2×#13108057 | C22 | semidirect |
| 16. C4⋊#11717579 | C22 | semidirect |
| 18. #15692167 | C22 | semidirect |
| 19. C4×#11717579 | C22 | semidirect |
| 21. C4⋊C8×C101 | C22 | semidirect |
| 23. C4×C8×C101 | C22 | semidirect |
| 53. C2×C4×C101 | M16 | semidirect |
| 89. C101 | #2975 | semidirect |
| 94. #431 | D101 | semidirect |
| 107. C4⋊C8 | C2×D101 | semidirect |
| 112. C4×C8 | C2×D101 | semidirect |
| 148. C2×C4 | #13108057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D404 | 2 |
| #20265256 | 2 |
| #20265254 | 2 |
| #20265230 | 2 |
| #20265139 | 2 |
| #431×C101 | 2 |
| #2975 | 101 |