Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#22548642 | C2 | semidirect |
| 3. #30631691 | C2 | semidirect |
| 4. #30631588 | C2 | semidirect |
| 5. #30631456 | C2 | semidirect |
| 6. #30631446 | C2 | semidirect |
| 7. #520×C251 | C2 | semidirect |
| 10. #22548740 | C4 | semidirect |
| 34. C2×D1004 | C2×C4 | semidirect |
| 41. #16860794 | C2×C4 | semidirect |
| 84. Q8×C251 | C22⋊C4 | semidirect |
| 88. D4×C251 | C22⋊C4 | semidirect |
| 132. C251 | #1883 | semidirect |
| 135. #520 | D251 | semidirect |
| 208. Q8 | (C2×D251)⋊C4 | semidirect |
| 216. D4 | (C2×D251)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| C2×#22548642 | 2 |
| #30631691 | 2 |
| #30631588 | 2 |
| #30631456 | 2 |
| #30631446 | 2 |
| #520×C251 | 2 |
| #1883 | 251 |