Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31774617 | C2 | semidirect |
| 2. D4×Dic542 | C2 | semidirect |
| 3. #31774255 | C2 | semidirect |
| 4. #31774248 | C2 | semidirect |
| 5. #31774191 | C2 | semidirect |
| 6. #31774177 | C2 | semidirect |
| 8. #31774102 | C2 | semidirect |
| 9. #31774027 | C2 | semidirect |
| 10. #31773994 | C2 | semidirect |
| 122. C271 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774617 | 2 |
| D4×Dic542 | 2 |
| #31774255 | 2 |
| #31774248 | 2 |
| #31774191 | 2 |
| #31774177 | 2 |
| #31774110 | 2 |
| #31774102 | 2 |
| #31774027 | 2 |
| #31773994 | 2 |
| C4×D8×C271 | 2 |
| #3367 | 271 |