Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20265377 | C2 | semidirect |
| 3. Q8×#11717579 | C2 | semidirect |
| 4. #20264929 | C2 | semidirect |
| 5. #20264921 | C2 | semidirect |
| 6. #20264920 | C2 | semidirect |
| 7. #460×C101 | C2 | semidirect |
| 46. Q8×C101 | D8 | semidirect |
| 66. #11717579 | SD16 | semidirect |
| 87. C101 | #1668 | semidirect |
| 90. #460 | D101 | semidirect |
| 133. Q8 | #13108059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265553 | 2 |
| #20265377 | 2 |
| Q8×#11717579 | 2 |
| #20264929 | 2 |
| #20264921 | 2 |
| #20264920 | 2 |
| #460×C101 | 2 |
| #1668 | 101 |