Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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. #30632863 | C2 | semidirect |
| 2. #30632854 | C2 | semidirect |
| 3. #30632844 | C2 | semidirect |
| 4. #30632841 | C2 | semidirect |
| 5. #30632840 | C2 | semidirect |
| 6. Q8×Dic503 | C2 | semidirect |
| 9. C2×C4⋊Dic503 | C2 | semidirect |
| 10. C4⋊C4×D503 | C2 | semidirect |
| 11. C22⋊Q8×C503 | C2 | semidirect |
| 37. C22⋊D503 | Q8 | semidirect |
| 74. C503 | #554 | semidirect |
| 81. C22⋊Q8 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632863 | 2 |
| #30632854 | 2 |
| #30632844 | 2 |
| #30632841 | 2 |
| #30632840 | 2 |
| Q8×Dic503 | 2 |
| C4×C22⋊D503 | 2 |
| (C22⋊D503)⋊C4 | 2 |
| C2×C4⋊Dic503 | 2 |
| C4⋊C4×D503 | 2 |
| C22⋊Q8×C503 | 2 |
| #554 | 503 |