Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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. #31774626 | C2 | semidirect |
| 3. #31774248 | C2 | semidirect |
| 4. #31774183 | C2 | semidirect |
| 7. C8×Q8×C271 | C2 | semidirect |
| 53. Q8×C271 | SD16 | semidirect |
| 74. C271 | #3359 | semidirect |
| 81. C8×Q8 | D271 | semidirect |
| 122. Q8 | #16864643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774626 | 2 |
| Q8×D1084 | 2 |
| #31774248 | 2 |
| #31774183 | 2 |
| #31774103 | 2 |
| C4×#16864643 | 2 |
| C8×Q8×C271 | 2 |
| #3359 | 271 |