Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22576183 | C2 | semidirect |
| 2. #31774569 | C2 | semidirect |
| 3. #31774274 | C2 | semidirect |
| 4. #31774134 | C2 | semidirect |
| 5. #31774097 | C2 | semidirect |
| 6. #31774045 | C2 | semidirect |
| 7. C8×D1084 | C2 | semidirect |
| 8. C4×Q16×C271 | C2 | semidirect |
| 48. Q16×C271 | D4 | semidirect |
| 88. C4×C271 | #135 | semidirect |
| 97. C271 | #3287 | semidirect |
| 105. C4×Q16 | D271 | semidirect |
| 138. Q16 | D1084 | semidirect |
| 187. C4 | #22576183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576183 | 2 |
| #31774569 | 2 |
| #31774274 | 2 |
| #31774134 | 2 |
| #31774097 | 2 |
| #31774045 | 2 |
| C8×D1084 | 2 |
| C4×Q16×C271 | 2 |
| #3287 | 271 |