Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#22548870 | C2 | semidirect |
| 2. C2×#22548867 | C2 | semidirect |
| 4. #30632797 | C2 | semidirect |
| 5. #30632788 | C2 | semidirect |
| 6. #30632784 | C2 | semidirect |
| 7. C22⋊Q8×C503 | C2 | semidirect |
| 27. C503⋊C8 | D4 | semidirect |
| 55. C503 | #468 | semidirect |
| 59. C22⋊Q8 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548870 | 2 |
| C2×#22548867 | 2 |
| #30632838 | 2 |
| #30632797 | 2 |
| #30632788 | 2 |
| #30632784 | 2 |
| C22⋊Q8×C503 | 2 |
| #468 | 503 |