Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20265547 | C2 | semidirect |
| 4. #20265546 | C2 | semidirect |
| 5. #20265545 | C2 | semidirect |
| 6. #20265544 | C2 | semidirect |
| 9. #491×C101 | C2 | semidirect |
| 86. D101 | #491 | direct (N × H) |
| 88. C101 | C2×#491 | semidirect |
| 95. #491 | D101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D101 | 2 |
| #125×D101 | 2 |
| #20265547 | 2 |
| #20265546 | 2 |
| #20265545 | 2 |
| #20265544 | 2 |
| #103×D101 | 2 |
| #97×D101 | 2 |
| #491×C101 | 2 |
| C2×#491 | 101 |