Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#15692263 | C2 | semidirect |
| 2. C22×#13108057 | C2 | semidirect |
| 4. #20265254 | C2 | semidirect |
| 5. #20265247 | C2 | semidirect |
| 6. #20265143 | C2 | semidirect |
| 7. #20265140 | C2 | semidirect |
| 8. #20265133 | C2 | semidirect |
| 9. #424×C101 | C2 | semidirect |
| 17. C2×#13108057 | C22 | semidirect |
| 19. C2×C8×D101 | C22 | semidirect |
| 26. #15692167 | C22 | semidirect |
| 27. #15692166 | C22 | semidirect |
| 28. C4×#11717579 | C22 | semidirect |
| 32. C4⋊C8×C101 | C22 | semidirect |
| 50. C2×#11717579 | D4 | semidirect |
| 114. C101 | #2930 | semidirect |
| 120. #424 | D101 | semidirect |
| 142. C4⋊C8 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692263 | 2 |
| C22×#13108057 | 2 |
| #20265689 | 2 |
| #20265254 | 2 |
| #20265247 | 2 |
| #20265143 | 2 |
| #20265140 | 2 |
| #20265133 | 2 |
| #424×C101 | 2 |
| #2930 | 101 |