Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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×D1084 | C2 | semidirect |
| 2. #31774256 | C2 | semidirect |
| 3. #31774247 | C2 | semidirect |
| 4. #31774192 | C2 | semidirect |
| 5. #31774177 | C2 | semidirect |
| 7. #31774099 | C2 | semidirect |
| 8. #31774028 | C2 | semidirect |
| 9. #31773995 | C2 | semidirect |
| 11. #556×C271 | C2 | semidirect |
| 122. C271 | #3367 | semidirect |
| 124. #556 | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1084 | 2 |
| #31774256 | 2 |
| #31774247 | 2 |
| #31774192 | 2 |
| #31774177 | 2 |
| #31774109 | 2 |
| #31774099 | 2 |
| #31774028 | 2 |
| #31773995 | 2 |
| C4×#16864639 | 2 |
| #556×C271 | 2 |
| #3367 | 271 |