Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. Q8×D404 | C2 | semidirect |
| 2. #20265523 | C2 | semidirect |
| 3. #20265457 | C2 | semidirect |
| 4. #20265369 | C2 | semidirect |
| 5. Q8×#11717579 | C2 | semidirect |
| 6. C4×#13108059 | C2 | semidirect |
| 7. #550×C101 | C2 | semidirect |
| 46. Q8×C101 | D8 | semidirect |
| 58. D404 | #41 | semidirect |
| 82. C101 | #3358 | semidirect |
| 83. #550 | D101 | semidirect |
| 129. Q8 | #13108059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D404 | 2 |
| #20265523 | 2 |
| #20265457 | 2 |
| #20265369 | 2 |
| Q8×#11717579 | 2 |
| C4×#13108059 | 2 |
| #550×C101 | 2 |
| #3358 | 101 |