Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #31773644 | C2 | semidirect |
| 5. #31773643 | C2 | semidirect |
| 6. #31773642 | C2 | semidirect |
| 7. #332×C271 | C2 | semidirect |
| 91. C271 | #1549 | semidirect |
| 99. #332 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D271 | 2 |
| #31773949 | 2 |
| #31773919 | 2 |
| #31773644 | 2 |
| #31773643 | 2 |
| #31773642 | 2 |
| #332×C271 | 2 |
| #1549 | 271 |