Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #30632453 | C2 | semidirect |
| 3. #30631669 | C2 | semidirect |
| 4. C2×#22548632 | C2 | semidirect |
| 5. #30631459 | C2 | semidirect |
| 6. #30631458 | C2 | semidirect |
| 7. C2×#100×C251 | C2 | semidirect |
| 38. #16860794 | D4 | semidirect |
| 58. M16×C251 | D4 | semidirect |
| 114. C251 | #1914 | semidirect |
| 120. C2×#100 | D251 | semidirect |
| 166. M16 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632453 | 2 |
| #30632254 | 2 |
| #30631669 | 2 |
| C2×#22548632 | 2 |
| #30631459 | 2 |
| #30631458 | 2 |
| C2×#100×C251 | 2 |
| #1914 | 251 |