Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20265525 | C2 | semidirect |
| 3. #20265464 | C2 | semidirect |
| 4. #20265377 | C2 | semidirect |
| 5. Q8×#11717579 | C2 | semidirect |
| 6. C4×#13108061 | C2 | semidirect |
| 7. Q82×C101 | C2 | semidirect |
| 46. Q8×C101 | SD16 | semidirect |
| 47. Q8×C101 | #41 | semidirect |
| 77. C101 | #3362 | semidirect |
| 78. Q82 | D101 | semidirect |
| 123. Q8 | #13108061 | semidirect |
| 124. Q8 | #13108075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265849 | 2 |
| #20265525 | 2 |
| #20265464 | 2 |
| #20265377 | 2 |
| Q8×#11717579 | 2 |
| C4×#13108061 | 2 |
| Q82×C101 | 2 |
| #3362 | 101 |