Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15692255 | C2 | semidirect |
| 3. #20265468 | C2 | direct (N × H) |
| 4. C2×#15692187 | C2 | semidirect |
| 6. C2×C4⋊C8×C101 | C2 | semidirect |
| 11. #15692255 | C22 | semidirect |
| 18. #15692187 | C22 | semidirect |
| 22. C4⋊C8×C101 | C22 | semidirect |
| 28. C2×D404 | Q8 | semidirect |
| 66. D404 | C2×Q8 | semidirect |
| 85. C2×C101 | #476 | semidirect |
| 91. C101 | C2×#476 | semidirect |
| 96. C2×C4⋊C8 | D101 | semidirect |
| 112. C4⋊C8 | C2×D101 | semidirect |
| 177. C2 | #20265468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692255 | 2 |
| C2×C4×D404 | 2 |
| #20265468 | 2 |
| C2×#15692187 | 2 |
| C2×#15692177 | 2 |
| C2×C4⋊C8×C101 | 2 |
| C2×#476 | 101 |