Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 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. Q8×Dic542 | C2 | semidirect |
| 3. #31774244 | C2 | semidirect |
| 4. #31774188 | C2 | semidirect |
| 5. #31774098 | C2 | semidirect |
| 6. C4×#16864643 | C2 | semidirect |
| 7. C8×Q8×C271 | C2 | semidirect |
| 46. Dic542 | #41 | semidirect |
| 55. Q8×C271 | SD16 | semidirect |
| 76. C271 | #3362 | semidirect |
| 83. C8×Q8 | D271 | semidirect |
| 124. Q8 | #16864643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic542 | 2 |
| #31774569 | 2 |
| #31774244 | 2 |
| #31774188 | 2 |
| #31774098 | 2 |
| C4×#16864643 | 2 |
| C8×Q8×C271 | 2 |
| #3362 | 271 |